probability book

Name:

Teacher:

ProbabMty

1: Outcomes Frequency

'. Heads L

w Ta ii S 24
ww
_____

Total 50

iJ

y e llow IIov Find the probability Head
of spinni ng yel low, Tails

- Head

Tails

_Pirit c:( )c ('Irpt 1!r %\ ptr tecn'
/

=3x2x2

Unit 5: Probability

TEK Description STARTERS QUIZ RETAKE OTHER OTHER OTHER OTHER MASTERED?
7.6A
7.6B represent sample spaces for simple and
7.6C compound events using lists and tree
7.6D diagrams
7.6E
7.6F select and use different simulations to
represent simple and compound events
7.6H
7.61 with and without technology

make predictions and determine
solutions using experimental data for
simple and compound events

make predictions and determine
solutions using theoretical probability
for simple and compound events

find the probabilities of a simple event
and its complement and describe the
relationship between the two

use data from a random sample to make
inferences about a population

solve problems using qualitative and
quantitative predictions and
comparisons from simple experiments

determine experimental and
theoretical probabilities related to
simple and compound events using
data and sample spaces

7.6P represent sample spaces for simple and compound events using lists and tree diagrams

Today we will loam how to draw tree diagrams to deterunne the number of outcomes

sessment How much do yon already Iwow about this topic? Bate YOMWN from 1-4

emm Beforn ______ After.

Intervention

/Challenge 5ee Googe Classroom

Level 1: Vocabulary:
What is the definition of
sample space, outcome, and - is any one of the possible results of an action. The set of
tree diagram? zi1I[ifl!4Icii

-_usesubranches Z show&al1lupossible ou

Example 1A (on your own): A coin is tossed twice. Make a list to show all

possible outcomes:

Level 2 Example 1B (with your teacher): A coin is tossedI[';Draw a ItreeZdiagram to

How do you know when

to start a new 'branch"?

Example 2A(with a partner): 10 colored beads are in a bag. Three are red, two
are blue, and five are green. You pick a bead from the bag, replace It, and
choose another bead. Make a list of the sample space.

Level 3 Example 2B (With your teacher): 10 colored beads are In a bag. Three are red,
Use the tree diagram or two are blue, and five are green. You pick a bead 1~om the bag, replace it, and
list to discover a way to choose another bead. Draw a tree diagram to make a list of the sample space.
find the total number of
outcomes without
constructing a list or
tree diagram.

Example 3: You go to a restaurant. You have a choice of sated, eggplant, or
pizza for your main course and ice cream or apple pie for dessert. Draw a tr,,-?

diagram and make a list of the sample space.

Level 4 Example 4: The Smith family has 8 children born in different years. Draw a tree
You can create a dgram and list the sample space to show all the possible combinations of boy
sample space by
and girl children in the family.
making a list or tree
diagram. Which way is
better? Explain Why.

Example 5: A cube, with faces numbered I tot, Is rolled and a penny is tossed at
the some time. Draw a tree diagram and make a list of the sample space.

Write a quick summary of what you learned:

2-

Sample Spaces and Tree Diagrams
Directions: Show all your work in your spiral!
1.)A cube, with faces numbered 1 to 6, is rolled, and a penny is tossed at the same time.
Draw a tree diagram and make a list of the sample space.
2.)Clayton has 3 fair coins. He flips the coin once. Draw a tree diagram and make a list of
the sample space showing what could happen with all three flips.
3.)The Smith family has 3 children born in 3 different years. Draw a tree diagram and
make a list of the sample space to show all possible arrangements of boy and girl children
in the Smith family.
4.)If Laquisha can enter school by any one of three doors and the school has 2 staircases to
the second floor, in how many ways can Laquisha reach a room on the second floor?
Justify your answer by drawing a tree diagram and making a list of the sample space.
5.)Kimberly has 3 pairs of pants: one black, one red, and one tan. She also has 4 shirts:
one pink, one white, one yellow, and one green. Draw a tree diagram and make a list of
the sample space that shows all possible outfits (an outfit consists of one pair of pants and
one shirt).
6.)Samuel is buying a new car. He wants either a convertible or hatchback. Both types of
cars are available in red, white, or blue and with automatic or standard transmission.
Draw a tree diagram and list the sample space of all possible choices of cars that are
available.
7.)You spinner a spinner that has 5 sections labeled 1, 3, 5, 7, and 9. You then spin a second
spinner that has 3 sections labeled A, B, and C. Draw a tree diagram and list the sample
space of spinning each spinner once.

3

NAME DATE PERIOD
SCORE
Practice 76(A)

Represent sample spaces for simple and compound events using lists and tree diagrams.

Multi-Step Example

Claire is ordering a milk shake. She has a choice of small, medium, or large, and vanilla or chocolate.
Make a tree diagram to determine the number of choices of milk shakes Claire can order.
Let S = small, M = medium, L = large, V = vanilla, and C = chocolate.

Size Flavor
Szz::

L-Z

The choices of milk shakes are listed below.

small, vanilla medium, vanilla large, vanilla
small, chocolate medium, chocolate large, chocolate

So, Claire has 6 choices of milk shakes.

1 Two number cubes labeled 1-6 are rolled. Which set 3 Which list shows all the different ice cream cone
represents the sample space for all the possible combinations when you choose one type of cone and
outcomes of the sum shown on both number cubes? one flavor of ice cream from the table below?

A {l, 2, 3, 4, 5, 61 Ice Cream Flavor i Cone Type
B 11, 2,3,4,5,6,7, 8, 9, 10, 11, 121 vanilla waffle
C {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 121 sugar
D {2, 3, 4, 5, 6, 7, 8, 9, 10, 111 chocolate
strawberry

2 Which set represents the sample space for all the A vanilla, waffle; chocolate, waffle; strawberry,
possible outcomes of tossing a coin twice? waffle

F {H, T} B vanilla, waffle; chocolate, waffle; vanilla, sugar;
G {HH, TT} chocolate, sugar
H {H, T, H, T}
J {HH, HT, TT, TH} C vanilla, waffle; chocolate, waffle; strawberry,
waffle; vanilla, sugar; chocolate, sugar;
chocolate, vanilla

D vanilla, waffle; chocolate, waffle; strawberry,
waffle; vanilla, sugar; chocolate, sugar;
strawberry, sugar

Course 2• Proportionality TX45

NAME DATE PERIOD
SCORE
Practice 7.6(A) (continued)

4 The flyer shows the choices for a scooter. How many 7 Which tree diagram shows the possible outcomes for
different scooters are available when choosing one T-shirts that come in the colors gray (G) or navy (N)
color, one power source, and one style? and in sizes small (S), medium (M), and large (L)?
F GM
Scooter World
NM
Color: red, green, blue
Power source: gas, electric G
Style: traditional, sporty
H
Record your answer and fill in the bubbles on your
answer document. Be sure to use the correct place
value.

5 The tree diagram shows all the possible outcomes for
which event?
<14 ':~~H

HT
TH

<14 _:Z~H IG S

TT 8 How many different combinations are there when
TH spinning the spinner twice?

F tossing a coin BLUE
G tossing a coin two times
H tossing a coin three times RED
I tossing two coins one time each
Record your answer and fill in the bubbles on your
6 Which shows the sample space for choosing one answer document. Be sure to use the correct place
crust type from thin (T) or hand tossed (H) and one value.
topping from pepperoni (P) or mushrooms (M)?

A {T, H, P, M}
B {TP, TM, HP, HM}
C {TP, HM}
D {TH, TP, TM, HP, HM, PM}

TX46 Course 2 - Proportionality

5

7.6 E Find the probabilities of a simple event and its complement and describe the relationship
between the two

-------------

Today we will learn bow to find the probability of simple events and the eomplement

Assessment flow much 10 Imalready know about this topic? Bate mirself from 1-4

II. IlthttI Beforn______ Mter.

Intervention

/Challenge 5ee Googe Classroom

Level i Vocabulary:

What is the Is the chance that some event Will occur. A
definition of
is one outcome or a collection of outcomes.
probability,

complementary The of an event Is a ratio that compares the number of

events, random, and favorable outcomes to the number of total outcomes.

simple event.

Outcomes occur at ________________ if each outcome is equally likely to occur.

are two events in which either one or the other must
happen, but they cannot happen at the same time. The sum of an event and its

complement is I or IOO.

Level 2 Examples:

How does the word i. What is the probability a person will spin...

"or" change the

probability question? a cap?

Whistle?

cap or yo-yo? o
a stuffed animal?
win a prize? rni !L", is"'
What is the complement of spinning a key ring?

2.7hereso Is taking a multiple-choice test and does not know an answer. She can
guess A, B, C, D. or E. What is the probability that Theresa will guess correctly?

3. A number cube is labeled I - 6. What is the probability orof lIling ri'i even .'ii
What Is the complement of rolling a 3?

to

Level 3 This spinner has different sized sections. 1I the iprobability of
1La1n!ding IonI'](!
Which color has the
same probability and i'Lthu
complement? How do
you know? lot MM71F=1i

Level 3:

yt . bq crtt'nc 6rr d, 1 kh and Pqrc rhIc.

ci nr:riJc be hc ici 1 ILmbc1 , nrblc

i: F prchL Ir indontl ' onc imchft reach cint

rmrfl 1JUChdflC1'YL

4L1'i WI t.!Fr;T;n;

The spinner shown is spun once. Determine the probability of each event
How likely is each event?

5,, if the ru icy iicertain color is o, wric- n epc in for

th Jitr :tc nd n n thtA ti n. i

P diiI . eee:pressonne'nH rhii reIt nship.

zlIW1IJH1HI FAKi)L'EEE3 =

1

NAME DATE PERIOD

Lesson I Skills Practice

Probability of Simple Events rji [B]
L2i
A card is randomly chosen. Determine each probability. p1
Express each answer as a fraction, a decimal, and a percent.

1.P(B)

2. P(Q or R) ILOJ
3. P(vowel)

4. P(consonant or vowel)

5.P(consonant or A)

6. P(T)

The spinner shown is spun once. Write a sentence dog dog
explaining how likely it is for each event to occur. (hamstN cat

7. P(dog) \L dog I cat

8. P(hamster)

9. P(dog or cat)

10.P(bird)

It. P(mammal)

The weather reporter says that there is a 12% chance that it will be moderately windy tomorrow.
12.What is the probability that it will not be windy?
13. Will tomorrow be a good day to fly a kite? Explain.

Course 2 - Chapter 5 Apply Proportionality to Probability

ill

NAME DATE PERIOD
SCORE
Cmh Practice 7.6(E)

Find the probabilities of a simple event and its complement and describe the relationship between the two.

Multi-Step Example

Aubrey has 4 red, 20 blue, 16 green, 2 yellow, and 10 black tiles. She randomly picks one tile. What is
the probability Aubrey picks a red or a yellow tile?
The favorable outcomes are red and yellow tiles. There are 4 red tiles and 2 yellow tiles. So, there are 6
favorable outcomes.
The total number of outcomes is 52 because there are 4 + 20 + 16 + 2 + 10 = 52 iles.
The probability of Aubrey picking a red or yellow tile is
number of favorable outcomes 6 3

- or
total number of outcomes - 52 26

1 Tessa is rolling a number cube labeled 1-6. What is 3 The table shows the number of marbles that Sammy
the probability of Tessa NOT rolling a 1, 2, 5, or 6? has in a bag. What is the probability that Sammy
A1 randomly pulls a green marble from the bag?

3 Marble Color Number in Bag
black 5
B1 purple 6
green 11
2 red 2
yellow 9
Cl
A1
3
3
6
B1
2 Miss Ward spins a wheel to determine the number of
homework problems to assign. There are 20 sections 2
labeled 1-20. What is the probability that there will be
fewer than 13 problems assigned for homework? C
3
F 13
20

6

11±

9

JL 4 Event A has a probability of 0.3. What is the
20 probability of the complement of Event A?

Record your answer and fill in the bubbles on your
answer document. Be sure to use the correct place
value.

Course 2 Proportionality TX6 I

NAME DATE PERIOD

____-_______

Practice 7.6(E) (continued)

5 Mrs. Valentine pulls names from ajar to determine 8 The table shows the number of jelly beans in a dish. If
who will be the line leader. There are 13 girls and 9 Jeremy randomly selects a jelly bean, what is the
boys in the class. What is the probability that a boy probability that is NOT lemon or orange?
will be the line leader?
Jelly Bean Type Number in Dish
F-- grape 10
22 lemon 8
orange 14
G 1—3 cherry 16
22
F!
H--
13 4

Ji 11
9 G-

6 Which two events are complements? 24
A spinning a 1 or a 2 on a spinner with 4 sections
labeled 1-4 2
B getting a head or a tail when tossing a coin
C rolling a 1 or a 2 when rolling a number cube 13
labeled 1-6
D drawing a red or green marble from a bag of red, 24
green, and yellow marbles
9 Savannah has one block for every letter of the
7 Sophia needs to spin a blue (B) or green (G) on her alphabet. What is the probability she picks a letter in
next turn to win a game. What is the probability, as a her name?
decimal, that Sophia wins the game on her next spin?
A-p-
26

B--
13

C
9

4

10 What is the sum of the probabilities of two
complementary events?

Record your answer and fill in the bubbles on your F—1
answer document. Be sure to use the correct place GO
value. H 0.5
JI

TX62 Course 2• Proportionality

7.61) make predictions and determine solutions using theoretical probability for simple and compound
events

-------------

Today we will learn how to find the probability of independent and dependent events.

Assessmrt How much do you already know about this topic? Rate yourself from 1- 4

Before: _________ After.

Intervention
/Challenge 5ee Googe Ctassroorn

Level 1: Vocabulary:
What is the definition of
theoretical probability, onis based uniform probability -what should happen when conducting a
simple event,
compound events, probability experiment.
independent events,
and dependent events?

I' is one outcome or a collection of outcome,

A consists of door more simple events. Some compound events not

affect each other's outcome. This is called...

events. Other compound events do affect outputs. These are called

events.

Level 2: Examples:
Categorize this question: 1. Two spinners are spun. What is the probability that both spinners will show an even
number?
Theoretical?
Simple? -
Compound?
Independent? "N
Dependent?

j

-

Categorize #2: 2. The game show contestant spins a spinner with the letters A through F on it, then either an easy or
hard question is picked randomly for her. What is the probability the spinner will stop on the letter D
and she is given a hard question?

Categorize #3:

3. You are about to attack a dragon in a role playing game. You will throw two dice, one numbered
Ito 7 and the other with letters A through C. What is the probability that you will roll a number
other than 6 and a letter after C?

Categorize #4: 4. There are 4 red, 8 yellow, and 6 blue socks in a drawer. Once a sock is selected, it is NOT
REPLACED, Find the probability that 2 blue socks are chosen.

Level 3: 5. There are 3 yellow, 5 red, 4 blue, and 8 green candies in a bag. Once a candy is pulled out of the
What would happen if jar it is not replaced. Find the probability of.....
you replaced the candy
after choosing the first? choosing 2 red candies

choosing 2 yellow candies

choosing a yellow followed by a blue

6. The names of boys and 10 girls from your class are put into a hat. What is the probability that
the first two names chosen will both be boys?

Summarize the difference between independent and dependent events:

12.

Name Date

Probability with Compound Events (Independent and Dependent)
Practice

Describe the events by writing I for independent event or D for dependent event.

1. Ann draws a colored toothpick from a jar. Without replacing it, she draws a second toothpick.
2. John rolls a six on a number cube and then flips a coin that comes up heads. ________
3. Susie draws a card from a deck of cards and replaces it. She then draws a second card.
4. Seth draws a colored- tile from a bag, replaces it; draws a second tile from the bag, replaces it; and then

draws a tile a third time from the bag.
5. You draw a red marble from a bag, and then another- red marble (without replacing the first marble)?

Using the two spinners, find each compound probability.

6. P(A and 2) 7. P(D and 1) 8. P(B and 3) 12
9. P(A and not 2)
0A 2

CB --

A box contains3 red marbles, 6 blue marbles, and 1 white marble. The marbles
are selected at random, one at a time, and are not replaced. Find each compound probability.

10. P(blue and red) 11. P(blue and blue) 12. P(red and white and blue)
13. P(red and red and red) -

14. P(white and red and white)

Suppose that two tiles are drawn- from the collection shown at the right. The first tile is Pq J Egg
replaced before the second is drawn. Find each compound probability.

15. P( A and A) 16. P(R and C) 17. P(A and not R)

Suppose that two tiles are drawn from the same collection shown above. The first tile is not replaced before
the second is drawn. Find each compound probability.

18. P(A and A) 19. P(R and C) 20. P(A and not R)

Use the spinner to the right for the next two problems.

21. If you spin the spinner twice, what is the probability of
spinning orange then -brown?

22. If you spin the spinner twice, what is the probability of
spinning brown both times?

23. Kevin had 6 nickels and 4 dimes in his pocket. If he took out one coin and then -a second coin without
replacing the first coin
(a) what is the probability that both coins were nickels?

(b) what is the probability that both coins were dimes?

(b) what is the probability that the first coin was a nickel and the second a dime?

Practice Probability with Compound Events - I

13

NAME DATE Ii[S1l]

Lesson 5 Skills Practice

Independent and Dependent Events

For Exercises 1-6, a number cube is rolled and the spinner at the right

is spun. Determine each probability. 2. P(odd and B)
1.P(1 and A)

3. P(prime and D) 4. P(greater than 4 and C)

5. P(less than 3 and consonant) 6. P(prime and consonant)

7. What is the probability of spinning the spinner above 3 times and getting a vowel each time?

8. What is the probability of rolling a number cube 3 times and getting a number less than 3 each time?

Each spinner at the right is spun. Determine each probability.
9. P(A and 2)

10. P(vowel and even)

11. P(consonant and 1)

12. P(D and greater than 1)

There are 3 red, 1 blue, and 2 yellow marbles in a bag. Once a marble is selected, it is not replaced. Determine each

probability. 14. P(blue and then yellow)
13. P(red and then yellow)

15. P(red and then blue) 16. P(two yellow marbles)

17. P(two red marbles in a row) 18. P(three red marbles)

There are 13 yellow cards, 6 blue, 10 red, and 8 green cards in a stack of cards turned face down. Once a card is

selected, it is not replaced. Determine each probability.

19. P(2 blue cards) 20. P(2 red cards)

21. P(a yellow card and then a red card) 22. P(a blue card and then a green card)

23. P(two cards that are not red) 24. P(two cards that are neither red or green)

Course 2 Chapter 5 Apply Proportionality to Probability

14

NAME DATE PERIOD

Lesson 5 Problem-Solving Practice

Independent and Dependent Events

1. In a game of checkers, there are 12 red game pieces and 2. What is the probability that the first piece is red and
12 black game pieces. Julio is setting up the board to the second piece is black? Explain how you
begin playing. What is the probability that the first two determined your answer.
checkers he pulls from the box at random will be two
red checkers?

For Exercises 3-5, use the following information.

Inger keeps her white and black chess pieces in separate bags. For each color, there are
8 pawns, 2 rooks, 2 bishops, 2 knights, 1 queen, and 1 king.

3. Are the events of drawing a knight from the bag of 4. Are the events of drawing a bishop from the bag of
white pieces and drawing a pawn from the bag of black white pieces and then drawing the queen from the
pieces dependent or independent events? Explain, same bag dependent or independent events? Explain.
Determine the probability of this compound event. Determine the probability of this compound event.

5. Determine the probability of drawing a pawn, a knight, 6. During a soccer season, Mario made approximately 2
and another pawn from the bag of white pieces. goal points for every 5 of his shots on goal. What is
the probability that Mario would make 2 goal points
on two shots in a row during the season?

Course 2 .Chapter 5 Apply Proportionality to Probability

15

NAME DATE PERIOD

Practice T6(D) SCORE

Make predictions and determine solutions using theoretical probability for simple and compound events.

Multi-Step Example

What is the probability of rolling an odd number when rolling a number cube labeled 1-6?
The favorable outcomes are the odd numbers, or 1, 3, and 5. There are 3 favorable outcomes.
The total number of outcomes is 6 because the number cube has 6 sides labeled 1-6.

number of favorable outcomes
P(odd number) =

total number of outcomes

= 3 or -1

-
62

So, the probability of rolling an odd number is

1 The tree diagram shows the sample space for tossing 2 Theoretically, how many times will the spinner land
a coin 3 times. What is the theoretical probability of a on the number 4 if it is spun 28 times?
coin landing heads up all three times?
Toss I Toss 2 Toss 3 Record your answer and fill in the bubbles on your
answer document. Be sure to use the correct place
H< value.
3 A spinner has 3 equal sections labeled green, blue,
<H H and red. What is the probability of landing on two
TT different colors when the spinner is spun twice?

A1 F1
8 4

B1 G1
3
4 9

Cl JI
9
2

P1
8

Course 2• Proportionality TX57

lu

NAME DATE PERIOD
SCORE
le Practice 7.6(D) (continued)

4 A card below is randomly selected. What is the 7 Reese tossed a coin and rolled a number cube labeled
probability it will be a 2 or 3? 1-6. What is the probability of tossing heads and
rolling an even number?
EEEEEEE
F1
A1 12
7
6
B1
H1
7 4

CI JI
3 2

B1 8 The table shows the possible sums when rolling two
4 number cubes labeled 1-6. What is the probability of
rolling a sum of 8?
5 A bag contains 12 blue, 7 green, and 9 orange
marbles. A spinner has 5 equal sections labeled 1-5. 123456
What is the probability of drawing a blue marble and 1234567
the spinner landing on 1? 23 4 5678
34 5 6 78 9
F1 4 5 6 7 8 9 10
28 5 6 7 8 9 10 ii
6 7 8 9 10 11 12
G1
A1
12 49

HI B1

35 36

7 C1
6
6 The table shows the pairs of socks in Lynn's drawer.
What is the probability of randomly selecting a pair of B1
white socks? 3

Color Number of Pairs 9 A spinner with 9 equal sections labeled 1-9 is spun
black 6 225 times. Theoretically, how many times will the
white 10 spinner NOT land on the number 7?
blue 4
gray 4 Record your answer and fill in the bubbles on your
answer document. Be sure to use the correct place
A1 value.
12

B1
4

Cl
12

B1
11

TX58 Course 2 Proportionality

11

7.bc

-L-e-d-m--i-n-g----- Today we will learn how to find experimental probability
TargeNC

Assessment I How much do you already know about this topic? Rate yourself from 1- 4

Before: __________ After:

Intervention

/Challenge See Google Ctassroorn

Level Q: Vocabulary:
What is the difference
between experimental The ratio of the number of times an event occurred to the total number of trials
& theoretical or times the activity is performed is called
probability?

E.. Ie 1: The graph shows the results of an experiment In which a number
cr i was rolled 100 times. Determine the experimental probability of rolling a 3

ihls experiment.

Cube

17,

10

Nu 5h

Example 2: in a telephone poll, 225 people were asked for whom they planned
to vote in a race for mayor. What is the experimental probability of Juarez
getting a vote from a person selected at random?

Level 3 Candidates u1n1)eI of Example 3: Suppose 5,700 people voted in the
How is experimental action. How many would you expect to vote
probability related to Juarez 73
proportions? Davis 67 for Juarez?
Abrainson 83

18

IF

2-xample 5: Suppose 600 students were surveyed. How many can be expected to
prefer dogs?
Example 6: Suppose 300 students were surveyed. How many can be expected to
*refer cuts?

11 111 1 1 11!111111! , l Jill 1111111 11 1 1 1 111 11

-A U0-

11

NAME DATE ll[S]

Lesson 2 Skills Practice Number Cube Experiment

Theoretical and Experimental Probability

1. A number cube is rolled 50 times and the results are shown in
the graph at the right.

a. Determine the experimental probability of rolling a 2.

b. 'What is the theoretical probability of rolling a 2?

c. Determine the experimental probability of not rolling a 2.

d. What is the theoretical probability of not rolling a 2?

e. Determine the experimental probability of rolling a 1.

2. Use the results of the survey at the right. What is Your Favorite
a. What is the experimental probability that a person's favorite Season of the Year?
season is fall? Write the probability as a fraction.
Sp ring 13% 39%
b. Out of 300 people, how many would you expect to say 25%
that fall is their favorite season? Summer
10%
c. Out of 20 people, how many would you expect to say that Fail
they like all the seasons?
Wintet
None, I lk-

them alt

d. Out of 650 people, how many more would you expect to say
that they like summer more than they like winter?

Course 2 • Chapter 5 Apply Proportionality to Probability

20

NAME DATE PERIOD

Lesson 3 Problem-Solving Practice

Make Predictions about a Population

For Exercises 1-3, use the table of results of Jeremy's survey 11 "11 NOrite People
of favorite kinds of movies. Type 12
Drama 3
Foreign 20
Comedy
15
Action 1

1. How many people did Jeremy use for his sample? 2. If Jeremy were to ask any person to name his or her
favorite type of movie, what is the probability that it
would be comedy?

3. If Jeremy were to survey 250 people, how many would 4. Survey results show that 68% of people tip their

you predict would name comedy? hairdresser when they get a haircut. Predict how many

people out of 150 tip their hairdresser.

5. A survey showed that 28% of adults play golf in their 6. Use the information in Exercise 5 to predict how many
free time. Out of 1,550 adults, predict how many adults out of 1,550 would say they do not play golf.
would say they play golf.

Course 2 Chapter 9 Statistics and Sampling

2I

Name: Experimental Probability Worksheet
Show your work!

Per:

1.) What is the theoretical probability that an even number will # on Cube Frequency
be rolled on a number cube? 1 8
2 3
2.) What was the experimental probability of how many times an 3 9
even number was actually rolled using the table? 4 6
5 4
3.) Theoretically if you roll a number cube 36 times, how many 6 6
times would you expect to roll the number one?

4.) How many times did you actually roll the number one in the experiment?

5.) What is the theoretical probability for rolling a number greater than 4?

6.) What was the experimental probability of rolling a number greater than 4?

7,) What is the difference between theoretical and experimental probability?

8.) If a car factory checks 360 cars and 8 of them have defects, how many will have
defects out of 1260?

9.) If a car factory checks 320 cars and 12 of them have defects, how many out of 560 will
NOT have defects?

10.) You plant 30 African violet seeds and 9 of them sprout. Use experimented probability to
predict how many will sprout if you plant 20 seeds?

11.) If you are picking a number between 1-20 what is the probability that you will pick a
number greater than 14 or less than 4?

12.) If you are picking a number between 1-20 what is the probability that you will pick an even
number or a multiple of three?

13.) If you are picking a number between 1-20 what is the probability that you will pick a
multiple of two or a number greater than 15?

14.)Amanda used a standard deck of 52 cards and I on
selected a card at random. She recorded the
suit of the card she picked, and then replaced %1,ts
the card. The results are in the table to the Spades
right.
Clubs

a.) Based on her results, what is the experimental probability of selecting a heart?

b.) What is the theoretical probability of selecting a heart?

c.) Based on her results, what is the experimental probability of selecting a
diamond or a spade?

d.) What is the theoretical probability of selecting ci diamond or a spade?

e.) Compare these results, and describe your findings.

15) bale conducted a survey of the students in his Eye Blue Brown Green Hazel
classes to observe the distribution of eye color. color
The table shows the results of his survey.
Number 12 58 2 8

a.) Find the experimental probability distribution for each eye color.

P(blue) P(brown) P(green)z P(hazel)

b.) Based on the survey, what is the experimental probability that a student in bale's
class has blue or green eyes?

c.) Based on the survey, what is the experimental probability that a student in bale's
class does not have green or hazel eyes?

d.) If the distribution of eye color in bale's grade is similar to the distribution in his
classes, about how many of the 360 students in his grade would be expected to
have brown eyes?

23

16.) Your sock drawer is a mess! You just shove all of your socks in the drawer without

worrying about finding matches. Your aunt asks how many pairs of each color you

have. You know that you have 32 pairs of socks, or 64 individual socks in four

different colors: white, blue, black, and tan. You do not want to count all of your

socks, so you randomly pick 20 individual Color of sock White Blue Black Tan
socks and predict the number from your

results. #ofsocks 12 13 4

a.) Find the experimental probability of each

P(white) = P(blue) = P(black) P (tan)

b.) Based on your experiment, how many socks of each color are in your drawer?

(white) (blue) (black) (tan)

c.) Based on your results, how many pairs of each sock are in your drawer?

(white) (blue) (black) (tan)

d.) Your drawer actually contains 16 pairs of white socks, 2 pairs of blue socks, 6 pairs of
black socks, and 8 pairs of tan socks. How accurate was your prediction?

Exercises 17 - 24: A single die is rolled. Find the theoretical probability of each.

17. P(3) = 18. P(9) = 19. P(even #)

20 P(a #>1) 21. P(a #<1) 22. P(a #<7)

23. P(a # divisible by 4) 24. P(a # 3 or greater)

Exercises 25 - 28: Find the odds in favor of each outcome if a single die is rolled.

25. A#3 26. A # divisible by 4

27. A # 3 or greater 28. Aneven#

24

I 8 0 4 04 4S •.
• 8
88 -- . •0
4.
J
- -

4, j 4, 8 S4 5, • 4 4 00

• I 8 - - 04 - SS -• -I
4 4 $S • •4
_1 • 4 44 *9 4 .4
•5 9V
J 4
•9
• 9• 0 •' 4 8 • $S •• ::
44 0 4S
•4 0 .____ I •4 4

94 49 • .0 5. •5 ••
9 4 4
4 I . 4 4.1 •
99 4 -w
4 •4 1 - I

Exercises 29 - 36: 2 dice are rolled Find the theoretical probability of each.
29. P(sum of 2) 30. P(sum of odd #) =

31. P(sum of even #) 32. P(sum > 6)

33. P(sum of < 10) 34. P(sum of <8)

35. P(sum of 11) 36 . P(sum of 5 or greater)

Exercises 37 - 46: Find the odds in favor of each outcome if 2 dice are rolled.

37. A sum of 2 38. A sum > 6

39. A sum < 10 40. A sum is an odd #

41. A sum is an even # 42. A sum < 8

43. A sum of 11 44. A sum of 7 or 11

45. A sum of 5 or greater 46. A sum of 4 or 9

25

NAME DATE PERIOD

Practice 7.6(C) SCORE

S0
Make predictions and determine solutions using experimental data for simple and compound events.

Multi-Step Example

The table shows the results of spinning the spinner 100 times. Find the experimental probability of
spinning 2 or 3.

31 Spinner Section Frequency
2\ 1 34
2
3 30
36

Find the number of times 2 or 3 was spun: 30 + 36 = 66.
Find the total number of times the spinner was spun: 34 + 30 + 36 = 100.

number of times 2 or 3 was spun
experimental probability =

number of times the spinner was spun

= 66 or 33
100
-

50

So, the experimental probability is 33

so

1 The table shows information about the type and 2 Raul tossed a coin and spun a spinner with three equal
number of sandwiches ordered by 80 customers. If sections. Based upon the results, what is the
120 customers order a sandwich, how many would probability of tossing a tail and spinning a 2?
you expect to order a club?
Coin Spinner Frequency
Sandwich Type Frequency heads 1 2
hamburger 24 heads 2 6
reuben 9 heads 3 7
club 36 tails 1 7
tuna salad 4 tails 2
chicken salad 7 tails 3 5

13

A36 10
I., '
C 54 G1

9

H1

8

J-230-

Course 2• Proportionality TX53

NAME DATE I1L]t

Practice 76(C) (continued) SCORE

3 Mackenzie made 38 of 50 free throws. What is the 6 Jewel spun a spinner and recorded the results in the
experimental probability that Mackenzie will NOT table. What is the experimental probability of the
make the next free throw she attempts? spinner landing on an even number?

25 Spinner Section Fretqquuuenuc. y
1 11
B 1-2 2 9
3 10
25 4 10
5 8
C1 6 12

25

D 21
25

4 Bryan conducted an experiment by tossing two coins. 15
Based upon his experiment, what is the probability of
tossing two heads or two tails? B--

Result Frequency 50
two tails 26
two heads 22 C
one head, one tail 52 2

D 31
60

F 11 7 Of 150 random customers, 63 ordered ham, 73
ordered turkey, and the rest ordered roast beef. Based
50 upon the results, how many of the next 75 customers
would you expect to order roast beef?
G 1-3 F5

50 G7

H 12 H 14
J28
25
8 Billy got 4 hits in his last 20 at-bats. Based upon this
13 information, how many hits would you expect Billy to
- get during his next 50 at-bats?

25 Record your answer and fill in the bubbles on your
answer document. Be sure to use the correct place
5 Of 100 random students surveyed, 42 own a dog, 34 value.
own a cat, 15 own a dog and a cat, and 9 own neither
a dog nor a cat. Based upon the results, how many of
the next 20 students surveyed would you expect to
own a dog and a cat?

Record your answer and fill in the bubbles on your
answer document. Be sure to use the correct place
value.

TX54 Course 2 • Proportionality

11

NAME DATE PERIOD

Practice 7.6(l) SCORE

Determine experimental and theoretical probabilities related to simple and compound events using data and sample
spaces.

Multi-Step Example

Gracie is playing a game and will randomly pick a tile from a bag. If the next tile she picks is a red or
blue tile, she will win the game. There are 25 green tiles, 20 red tiles, and 35 blue tiles. How much
greater is the probability that Gracie will win the game than the probability she will not win the
game?

number of favorable outcomes
P(green tile) =

total number of outcomes

25

- 25 +20+3S

5
16

number of favorable outcomes
P(red or blue tile) =

total number of outcomes

20+35

- 25+ 20 + 3S

11

16

So the difference in the probabilities is 11 -5o3r-

--

16 16 8

1 Andy spun the spinner 30 times. The spinner landed on 2 Missy rolls two 6-sided number cubes labeled 1-6.
the orange section 10 times. What is the difference What is the probability that both number cubes land on
between the theoretical and experimental probabilities a prime number?
of the spinner landing on the orange section?
F1
(.......................... . 36

Yellow Orange G

Green 0 Red 4

Purple Hi

15 3

B 1
5
3
C
3 Jake rolls a 6-sided number cube labeled 1-6 twice. To
3 the nearest hundredth, what is the probability that the
first roll is 4 and the second roll is an even number?
2
Record your answer and fill in the bubbles on your
Course 2• Proportionality answer document. Be sure to use the correct place
value.

TX77

Is

NAME DATE PERIOD

Practice 7.6(I) (continued) SCORE

4 The probabilities of selecting marbles from ajar are 6 Isaac is playing a dart game at the school carnival. The
shown in the table. There are 5 green marbles in the dartboard is shown. How much greater is the
jar. What is the minimum number of marbles in the probability of Isaac hitting a gray square than a black
jar? square?

Marble Color Probability
blue 101-
white

clear 2-

A 25 marbles A-i-
25
B 20 marbles
B 33
C 5 marbles 25

D 4 marbles c--
25
5 Allie is deciding when to take her vacation. She wrote
each month of the year on a separate piece of paper 25
and put the pieces in an envelope. The table shows the
results of picking a piece of paper from the envelope. 7 Tom put slips of paper with numbers ito 50 in a hat.
What is the experimental probability that Allie will As a decimal, what is the theoretical probability that
take her vacation during a month that starts with a Tom will choose a slip of paper with a number that is
NOT greater than 10 or less than 35?
Month Frequency Month Frequency Record your answer and fill in the bubbles on your
Jan. 9 July 4 answer document. Be sure to use the correct place
Feb. 6 Aug. 9 value.
Mar. 12 Sept. 15
April 6 Oct. 5 8 Linda rolled two 6-sided number cubes labeled 1-6
May 7 Nov. 9 fifty times. She rolled a sum of 6 fifteen times. What is
June 10 Dec. 8 the experimental probability of a sum of 6?

F 13 F 0.15
100 G 0.25

G-- H 0.3
50
10.5
H 19
100

23

100

TX78 Course 2• Proportionality

29

NAME DATE PERIOD

Practice 7.6(F) SCORE

SV
Use data from a random sample to make inferences about a population.

Multi-Step Example

Sophia filled a piñata with 500 pieces of candy. After the piñata broke, Robert filled a bag with the
types of candy shown in the table. Based on the sample in Robert's bag, how many Gummy Rings
and Lollipops were in the piñata?

Type of Candy Number in Bag
chocolate bars 2
gummy rings 5
lollipops 4
bubble gum 6
licorice 3

5+4 =9 Find the number of Gummy Rings and Lollipops in Robert's bag.
2 + 5 + 4 + 6 + 3 = 20 Find the total number of pieces of candy in Robert's bag.
Write a proportion, where x is the number of Gummy Rings and Lollipops in the
= ...L piñata.
Cross multiply.
20 500 Simplify.
Divide each side by 20.
9 500 = 20 x
Simplify.
4,500 = 20x
40O = 20x

20 20

225 = x

So, there were approximately 225 Gummy Rings and Lollipops in the piñata.

1 The table shows the results of a school survey about 2 Mama Mia's Pizzeria had random customers sample
favorite frozen yogurt flavors. If there are 432 students their new spaghetti sauce. Of the customers that
in the school, predict how many would select vanilla or sampled the new sauce, 42% liked the new sauce, 37%
strawberry as their favorite flavor. liked the old sauce, and 21% could not tell a
difference. Based on this information, how many of
Flavor Number of Votes their 1,250 customers will like the new spaghetti
vanilla 7 sauce?
chocolate 3
strawberry 4 F 2,976 customers
other 10
G 525 customers
A 72 students
B 126 students H 462 customers
C 198 students
D 942 students J 262 customers

Course 2• Proportionality TX65

30

NAME ---- DATE PERIOD
SCORE
Practice 7.6(F) (continued)

3 The table shows the results of a survey for an election 6 Bessie has a bag of 300 marbles. She grabbed a
for class president. Based on the data, if there are 336 handful of marbles from the bag. There were 1 red, 4
students voting, approximately how many more will orange, 2 purple, and 3 green marbles in her hand.
vote for Allie than for Olivia? Based on the sample, how many red and orange
marbles are in the bag?

Candidate Number of Votes A 30 marbles
Tom 2 B 120 marbles
Allie 10 C 150 marbles
Olivia 7 D 200 marbles
Adam 5

A 42 students 7 A baby giraffe was born at a zoo. Each visitor during
B 98 students the week voted on the name of the baby giraffe. The
C 112 students results of the first day are shown in the table. If there
D 140 students are 2,500 visitors that will get to vote, approximately
how many votes will be for the name Talia?

4 The manager of a landscaping company randomly Name Number of Votes
selected a sample of receipts from last year and found Zola 52
that 17 customers bought azaleas, 26 customers bought Nala 113
pansies, and 7 customers bought geraniums. Based on Talia 85
the sample, estimate how many of the 4,750 customers
last year bought azaleas and geraniums. F 735 votes
G 850 votes
Record your answer and fill in the bubbles on your H 1,650 votes
answer document. Be sure to use the correct place J2,125 votes
value.
8 The city council is trying to decide if a stoplight
5 A fisherman took a sample of fish with a large fishing should be installed at an intersection. Of the people
net from a lake. In the net there were 15 bass, 12 trout, polled, 124 do not want a stoplight installed, 514 want
8 blue gill, and 11 catfish. There are an estimated a stoplight installed, and 87 people are indifferent. If
10,000 fish in the lake. Based on the sample, how there are 15,800 people in the city, predict how many
many of those fish are catfish? more people would want a stop light compared to the
number who would not want a stoplight.
F 1,789 catfish
G 2,391 catfish A 390
H 2,981 catfish
J 7,459 catfish

C 8,500
D 9,306

1X66 Course 2• Proportionality

31

DATE

Practice 7.6(H) SCORE

Solve problems using qualitative and quantitative predictions and comparisons from simple experiments.

Multi-Step Example

The table shows the number of bottles of nail polish in a bag. How many times would you expect to
select purple nail polish if you picked a bottle of nail polish from the bag 120 times and replaced it
each time? Explain.

Color of Nail Polish Number of Bottles
Pink 7
Purple 9
Green 1
Red 3
Sparkles 7

The probability of picking a purple bottle is number of favorable outcomes = -29 7or3-1
total number of outcomes

So, you can expect to pick a purple bottle of nail polish • 120 or 40 times.

3

1 Scarlett is making a card. She has a drawer with 3 red, 3 How many times would you expect the spinner to
2 pink, 5 green, 1 white, and 4 purple pieces of paper. NOT land on Red if the spinner is spun 40 times?
How likely is it that Scarlett will randomly select a Justify your prediction.
pink piece of paper?
Yellow Blue
A unlikely
Blue \Red
B as likely to happen as not Yellow

C likely A 8 times' 5x 40 is 8.

D certain B 16 times 2 x 40 is 16.

2 Heather has a bag of 15 red, 11 orange, 9 yellow, 12 -
green, 6 blue and 11 purple markers. How many times
would you expect Heather to pick a red marker if she 5
picked a marker 90 times?
C 24 times x 40 is 24.
F about 11 times
'5
G about 15 times
D32 times ±x 40is32.
H about 21 times
'5
J about 64 times
TX73
Course 2 Proportionality

32

NAME DATE PERIOD

1~w Practice 7.6(H) (continued) SCORE

4 Tony has a workout playlist consisting of 4 songs for 7 The table shows the number of different color balloons
stretching, 14 songs for running, and 6 songs for set up for a dart game at a carnival. Which statement is
lifting weights. If the playlist is shuffled, how likely is true?
it a randomly selected song will be a song for running?
Balloon Color Number of Balloons
F impossible red 5
yellow 6
G as likely to happen as not orange 5
green 4
H likely blue 1
purple 4
J certain
F The probability of hitting a red balloon is as likely as
5 Justin is tossing a quarter to determine which team gets hitting a yellow balloon.
the ball at the beginning of a football game. The Rams
get the ball if the quarter lands on heads and the Tigers G The probability of hitting a blue balloon is greater
get the ball if the quarter lands on tails. How likely is than hitting the other color balloons.
it that the Rams will have the ball at the beginning of
the game? H The probability of hitting a yellow balloon is less
than hitting the other color balloons.
A unlikely
J The probability of hitting a green balloon is as likely
B as likely to happen as not as hitting a purple balloon.

C likely 8 Ava writes each letter of the alphabet on separate note
cards and puts the cards in a hat. How many times
D certain would you expect Ava to pick a letter from her name if
she picks a card 50 times, returning the card to the hat
6 Sam is renting a car for vacation. The table shows the each time?
number of keys in a bag for each type of car in the
parking lot. How many times would you expect Sam A about 2 times
to randomly select keys for a convertible or a sports
car if he selects a key 120 times?

B about 4 times

Type of Car Number of Keys in Bag C about 13 times
SUV 7
sedan 16 D about 26 times
convertible 2
compact 12 9 Elaina misses 2 free throws for every 10 attempts.
sports 3 How many free throws can you expect Elaina to make
if she shoots 15 free throws in a game?

Record your answer and fill in the bubbles on your Record your answer and fill in the bubbles on your
answer document. Be sure to use the correct place answer document. Be sure to use the correct place
value. value.

TX74 Course 2 - Proportionality

33

- Und --,jnd events with and without

tecK

-iediñi ---1 Today we will learn how to create a simulation
i. Targetsk:

Assessment How much do you alrea1y know about this topic? Rate yourself from 1- 4
I1,J!I(!1

Before: _________ After:

Intervention

/Challenge See Google Classroom

Vocabu
Simulation

Why do you think simple Examples:
simulation experiments
are not used often? I A cereal company is placing one of eight different trading cards in its boxes of cereal. If each

I card is eqatly likely to appear in a box of cereal, describe a model that could be used to

simulate the cards you would find in 15 boxes of cereal.

A restaurant is giving away 1 of 6 different toys with its children's meals. if the toys are
given out randomly, describe a model that could be used to simulate which toys would be
given with 6 children's meals.

Mr. Hawkins needs to choose 5 students at random from his homeroom to serve on the
school's activity committee. if there are 24 students in his homeroom, describe a model that
he could use to simulate choosing these 5 students.

Rodotfo must wear a dress shirt and a tie when he works at the mall on Friday Saturday.
and Sunday. Each day he picks one of his 5 dress shirts and 2 ties at random. Describe a
model that Rodolfo could use to simulate his selection of a shirt and tie.

Write your own simulation problem:

34