PACE Probability Unit

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Teacher:_____________________
ProbabMty

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Unit 5: Probability

TEK Description STARTERS QUIZ RETAKE OTHER OTHER OTHER OTHER MASTERED?
76A
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 with and without technology
761
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

After Lesson r 1
Rating: After Practice
Rating: !s: YES

F- I PA

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

The Sample Space is the set

I of all possible outcomes. I

I.................

A diagram that shows all l"1

I possible outcomes. T t'r'

1 1 ir

I .. . L_
.
•

First Coin Second Coin Third Coin Outcomes
HHH
When drawing a tree diagram H
HHT
ask yourself what could ) NT HTH

happen! H HU
THH
T
THT
iY 27A coindoesn't have I TTH
H
numbers, so you
H
\) shouldn' have any
t you r tree

m

• 1.) You go to a restaurant. You have a choice of salad, eggplant, •
or pizza for your main course and ice cream or apple pie for

I dessert. Draw a tree diagram and list all possible outcomes.

2.) The smith family has 3 children born in different years. Draw •
a tree diagram and list all possible outcomes of boy and girl

I children in the Smith family.

'3.) A cube, with faces numbered 1 -6, is rolled and a coin is
ossed at the same time. Draw a tree diagram and list all the

LCoutcomes of tossing the number cube and flipping the coin.
0 •0 0

2

U-j V

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.

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).

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.

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__________________

Practice 7.6(A) SCORE

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

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
outcomes of the sum shown on both number cubes? combinations when you choose one type of cone and

one flavor of ice cream from the table below?

A {1,2,3,4, 5, 61 FMI iic tYl)c
B {1,2,3,4,5,6,7, 8, 9, 10, 11, 121 Icc (:(111] Flax
C {2,3, 4, 5, 6, 7, 8, 9, 10, 11, 121
D 12, 3,4,5, 6, 7, 8, 9, 10, 111 vanilla waffle

chocolate sugar

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 4
SCORE
e, Practice 76(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)?

Scooter World F GM
NM
Color: red, green, blue
Power source: gas, electric
Style: traditional, sporty

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

5 The tree diagram shows all the possible outcomes for
which event?
H

H<

<TH IG S

F tossing a coin 8 How many different combinations are there when
G tossing a coin two times spinning the spinner twice?
H tossing a coin three times
I tossing two coins one time each BLUE

6 Which shows the sample space for choosing one RED
crust type from thin (T) or hand tossed (B) and one
topping from pepperoni (P) or mushrooms (M)? Record your answer and fill in the bubbles on your
answer document. Be sure to use the correct place
A{T,H,P,M} value.
B {TP, TM, HP, HM}
C {TP, RM}
B {TH, TP, TM, HP, IM, PM}

TX46 Course 2• Proportionality

5

Name:

4b 4b

' ti "The probability of the event A I

AV happening q PIMA, MT, SINSGOR(M

4D 4D ,,

0 Oil,

0

a scenario that involves or an A box of donuts contains 6 sprink!ed, 3
uncertain result & can have different
coconut, and 3 chocolate donuts. If you

reach in and pull one out without looking,

what is the probability that you get a

the of a single chocolate donut? (1/4 is less
performance of an experiment 4 than half,
so it's not
a particular outcome of an
4 as likely as
nn_%%p Bo n
getting a
sprinkled

donut

', Lbwouled )

10111 Li

ProbObitY is always

between zero and one

a measure of

a particular event is

,41 -

2015 Ma raff

Find the probability of Find the probability of Find the probability of
getting heads" on rolling both even
rolling an even number on
three coin flips in a row. numbers when you roll
4P a standard 6-sided die. Ways the event can occur: two 6-sided dice at once.
Ways the event can occur:
O Possible outcomes.

-. Probability: (

gj rolling a 2, a 4, or a 6 (3 ways)
Possible outcomes-

rolling al,2, 3, 4, 5, or6(o total)

Probability: / (
- Simplify:
L

NAME DATE PERIOD 6

Lesson I Skills Practice FA RB R

Probability of Simple Events 1F-K] 1Q71 E
[2J
A card is randomly chosen. Determine each probability.
Express each answer as a fraction, a decimal, and a percent.

1.P(B)

2.P(QorR)

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 clog I dog
explaining how likely it is for each event to occur.

7. P(dog)

8. P(hamster) \ dog
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

NAME DATE PERIOD 7

Practice 7.6(E) SCORE

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

11± 4 Event A has a probability of 0.3. What is the
probability of the complement of Event A?
9

1

20

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

Course 2 Proportionality TX6I

NAME 8

DA PERIOD

5e Practice 7.6(E) (continued) SCORE

5 Mrs. Valentine pulls names from ajar to determine 8 The table shows the number ofjelly 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 1 Number in fish
22 grape 10
lemon 8
G 13 orange 14
22 cherry 16

13 F

jI 4
9
G 11
6 Which two events are complements? 24
A spinning a I or a 2 on a spinner with 4 sections
labeled 1-4 H
B getting a head or a tail when tossing a coin
C rolling a 1 or a 2 when rolling a number cube 2
labeled 1-6 13
O 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?
26

13

C

9

aWll, FA 4

rleAoi~ 10 What is the sum of the probabilities of two
complementary events?
I
F—1
Record your answer and fill in the bubbles on your GO
answer document. Be sure to use the correct place 11 0.5
value. JI

TX62 Course 2 Proportionality

9

'B efore' u:
Ar l w
Afte,r Pr

ee ttr!s: YES tlô 0 ass=

I A number cube is
rolled. What is the
-- - ---------- Just • 1 probability it will land
on a prime number or
Simplify., ( 4?

I An event that consists of exactly one outcome

._ - - --- ----- -

Multipi

1F - - - - - - - - - - - - - - - - - - - - - - - - - - --

I An event that has more than one outcome. I

.............................. d

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

An event that is not affected by another I I The outcome of the first event affects I

1 event. I the outcome of the others.. I
.- - - - - - - - - . . - - - - -

own

00

MI There are 4 red, 8 yellow,

A number cube is rolled 6 blue, blue socks in a

twice. What is the 4 drawer. Once a sock is
probability it will land on
selected it is not

an even number on the replaced. What is the

first roll and a 3 on the ""'I/ probability of choosing 2

second roll? blue socks? 00

4

10

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) 1
9. P(A and not 2) 2
- 2

0A

. CB
-. .

A box. contains 3 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 N99. 99
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)

Supposethat 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

11

NAME DATE

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.

LP(l and A) 2. P(odd and B)

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, I 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

NAME DATE PERIOD 12

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

13

NAME DATE PERIOD

Practice 7.113(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?
Record your answer and fill in the bubbles on your
Toss I Toss 2 Toss 3 answer document. Be sure to use the correct place
value.
< 3 A spinner has 3 equal sections labeled green, blue,
H HT and red. What is the probability of landing on two
different colors when the spinner is spun twice?
H
F1
<H 4
3
TT 9

A1 JI
8 9

B1

4

Cl

2

8

Course 2• Proportionality TX57

NAME DATE PERIOD 14

Practice 76(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?
NEI I I 10 F1

A 12
7
6
B
7 'Ii

Ci 4
3
Ji
4 2

5 A bag contains 12 blue, 7 green, and 9 orange 8 The table shows the possible sums when rolling two
marbles. A spinner has 5 equal sections labeled 1-5. number cubes labeled 1-6.'What is the probability of
What is the probability of drawing a blue marble and roiling a sum of 8?
the spinner landing on 1? .1 2 3 4 5 6
12 3 4567
26 23 45678
34 5 6 7 8 9
12 4 5 6 7 8 9 10
5 6 7 8 9 10 11
Ji 6 7 8 9 10 11 12

7 A1
49
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? 36

Color Number of Pairs C
black 6 6
white 10
blue 3
4
gray 4 9 A spinner with 9 equal sections labeled 1-9 is spun
225 times. Theoretically, how many times will the
A1 - spurner NOT land on the number 7?
12
Record your answer and fill in the bubbles on your
B answer document. Be sure to use the correct place
value.
4
Course 2 Proportionality
12

11

TX58

15

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40 40

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bar graph r

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• What actually hannens I

I when you nerlorm the /1I under normal A • -.
exuierinient.
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4 VX41 K heThore you perforn
the experiment, the

L 4. closer you get to

y.theoretical probabilit !

L — — ——

I —T—he—g—ra—ph—s—ho—w—s —an—e—xp—eriment in wch a number

I cube was rolled 100 times. Determine the I
I experimental probability of rolling a 3 in this I
I
I experiment. Compare it to the theoretical
Number Cube Experiment probability of rolling a three.

25 --------------- ——

20

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lto C 9Lr

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£ ————————————————————————

Candidates Number of I In a telephone poll, people were asked who they were voting for.

Juarez Fepl What is the probability Juarez gets a vote from a person at random? I
Davis
7:
Abramson
67 I If 5,7000 voted in the election, how many would you expect to vote I
_____
I

-----------------------I

NAME DATE 1612-1ma

I]iWIt'It 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 s Your favorite
a. What is the experimental probability that a person's favorite
season is fall? Write the probability as a fraction. Ir Season of the Year?

b. Out of 300 people, how many would you expect to say Spring L_ 13% 39%
that fall is their favorite season? Summer LI
13% 25%
c. Out of 20 people, how many would you expect to say that Fall i 10%
they like all the seasons?
Winter ,
None,like

them all

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

NAME DATE PERIOD 17

I*i.]iCI JT1 1 1W1IiT!U

For Exercises 1-3, use the table of results of Jeremy's survey Favorite \1oie type
of favorite kinds of movies.
Type People

Drama 12

Foreign 3

Comedy 20

Action 15

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

18

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 car's 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?

19

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 Diamonds Jit1J I
selected a card at random. She recorded the
suit of the card she picked, and then replaced Hart
the card. The results are in the table to the
right. ~ Spa I
LL,I__________
d
L

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 a 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) 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?

20

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 an
socks and predict the number from your

results. #ofsocks 12 1 3 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. An even #

HHH 21
H H IEY

H 1 ii 111

-011FW to 61A Jul11

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

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

NAME DATE PERIOD 22

Practice 7.6(c) SCORE

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.

Spinner Section Frequency
1 34
2 30
36
3

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 33
= - or -

LOU 50

So, the experimental probability is 33

-
50

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 F-i-

C 54 10
D63
9

8

J--

20

Course 2 Proportionality 1X53

DATE PERIOD 23

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?

A-- SpinnerSection: Frequency
1 11
25 2 9
12 3 10
25 4 10
5 8
ci 6 12
25
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-9-

Result Frequency 50
two tails 26
two heads 22 C
one head, one tail 52
2
31
60

F 11 7 Of 150 random customers, 63 ordered ham, 73
50 ordered turkey, and the rest ordered roast beef. Based
13 upon the results, how many of the next 75 customers
50 would you expect to order roast beef?
12 F5
25 G7
13 H 14
25 J28

S Of 100 random students surveyed, 42 own a dog, 34 8 Billy got 4 hits in his last 20 at-bats. Based upon this
own a cat, 15 own a dog and a cat, and 9 own neither information, how many hits would you expect Billy to
a dog nor a cat. Based upon the results, how many of get during his next 50 at-bats?
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
Record your answer and fill in the bubbles on your value.
answer document. Be sure to use the correct place
value.

TX54 Course 2 Proportionality

24

NAME DATE PERIOD

Practice 76(l) SCORE

SV

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?

P(green tile) = number of favorable outcomes

total number of outcomes

25

25 +20+35
5
16

P(red or blue tile) number of favorable outcomes

total number of outcomes

20+3S

2S+20+35

11

-

16

So, the difference in the probabilities IS 11 1-56or38-
1- 6-

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?
F-316-
Yellow Orange
G 2:
Green 0 Red
4
Purple
3
15
ji
B
3
ci
3 3 Jake rolls a 6-sided number cube labeled 1-6 twice. To
the nearest hundredth, what is the probability that the
2 first roll is 4 and the second roll is an even number?

Course 2 Proportionality Record your answer and fill in the bubbles on your
answer document. Be sure to use the correct place
value.

TX77

NAME DATE PERIOD 25

Practice 7.6(I) (continued) SCORE

4 The probabilities of selecting marbles fi-orn 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
white 11- 0

clear 2-

A 25 marbles 25

B 20 marbles 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 J? Tom will choose a slip of paper with a number that is
NOT greater than 10 or less than 35?
Month Frequency Month Frequency
Jan. 9 July 4 Record your answer and fill in the bubbles on your
Feb. 6 Aug. 9 answer document. Be sure to use the correct place
Mar. 12 Sept. 15 value.
April 6 Oct. 5
May 7 Nov. 9 8 Linda rolled two 6-sided number cubes labeled 1-6
June 10 Dec. 8 fifty times. She rolled a sum of 6 fifteen times. What is
the experimental probability of a sum of 6?
F 13
-- F 0.15
100
G 0.25
50
110.3
H 19
100 JO.5

23

100

TX7B Course 2 Proportionality

NAME DATE_____ PERIOD 26

Practice 7.6(F) SCORE

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
lollipops 5
bubble gum
licorice 4
6
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
= piñata.
20 500 Cross multiply.
Simplify.
9 500 = 20 x Divide each side by 20.

4,500 = 20x Simplify.

4,500 = 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 II 462 customers
C 198 students
D 942 students J 262 customers

Course 2 Proportionality 1X65

NAME DATE PERIOD 27

Practice7.6fl (continued) SCORE
1144~r

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
pansies, and 7 customers bought geraniums. Based on Talia 113
the sample, estimate how many of the 4,750 customers
last year bought azaleas and geraniums. 85

Record your answer and fill in the bubbles on your F 735 votes
answer document. Be sure to use the correct place G 850 votes
value. H 1,650 votes
J2,125 votes
5 A fisherman took a sample of fish with a large fishing
net from a lake. In the net there were 15 bass, 12 trout, 8 The city council is trying to decide if a stoplight
8 blue gill, and 11 catfish. There are an estimated should be installed at an intersection. Of the people
10,000 fish in the lake. Based on the sample, how polled, 124 do not want a stoplight installed, 514 want
many of those fish are catfish? a stoplight installed, and 87 people are indifferent. If
there are 15,800 people in the city, predict how many
F 1,789 catfish more people would want a stop light compared to the
G2,391 catfish number who would not want a stoplight.
H 2,981 catfish
J 7,459 catfish A390

I:i:isr.i

C 8,500
P 9,306

TX66 Course 2• Proportionality