JDM Chap 8 Combine

Unit Matematik

Kolej Matrikulasi Johor
Kementerian Pendidikan Malaysia

JOM-DO-MATH (JDM)
Chapter 8 Probability( Set 1 )

1. A and B are two events P(A)  1 , P(B)  2 and P(A  B)  3 . Determine whether A
43 4

and B are independent event.

2. The probability of two event A and B are P(A)  0.3and P(B)  0.5 . Find P(A  B) if

(a) A and B are mutually exclusive
(b) A and B are independent.
3. Suppose A and B are two events with P(A)  0.1and P(B)  0.8 . Find

(a) P(A  B) if A and B are independent.

(b) PA B if P(A  B)  0.7

4. If P(X )  0.2 , P(Y )  0.5 and P(X Y )  0.1, find

(i) P(X Y ) (ii) P(X Y ) '

(iii) PX Y  (iv) PY X 

(v) P(X 'Y ') (vi) P(X 'Y )
(viii) P(X 'Y ')
(vii) PY X '

5. A, B and C are three events such that P(A)  1 , PA B  1 , PB A  2 , P(C ')  7
6 3 3 12
and P(A  C)  7
12
(a) Find (i) P(A  B) (ii) P(A  B) (iii) P(A  C)

(b) Determine whether events
(i) A and B are mutually exclusive ,
(ii) A and B are independent,
(iii) A and C are mutually exclusive ,
(iv) A and C are independent

BKS 2019/20 Page 1

Unit Matematik
Kolej Matrikulasi Johor
Kementerian Pendidikan Malaysia

LO-MED-UP
Chapter 8 Probability( Set 2 )

1. A group of 80 people was asked which three meats, fish, beef or mutton they consume.
The results show that 38 consumed fish, 28 consumed beef and 39 consumed mutton, 14
consumed both fish and beef, 10 consumed fish and mutton, 8 consumed mutton and beef
and 4 abstained from taking any sort of meats.
(a) Find how many people consumed all types of meats. Hence represent the information
in a Venn diagram.
(b) Find the probability that a person selected at random from this group consumed
(i) at least one of the meat
(ii) only one of the meat,
(iii) all the meats.

2. A statistical survey found that 90% of the employees are happy with their work given that
they received performance bonus, while 50% of employee are not happy with their work
given that they do not received performance bonus. If 80% employees received a
performance bonus, find the probability that an employee chosen does not receive bonus
given that he is happy with his work.

3. A box has 3 white balls and 5 black balls. 2 balls are randomly taken out of the box, one
at time. If the first ball is a white ball, the ball is returned to the box. If the first ball is black
ball, the ball is removed from the box. Find the probability that two balls are of
(a) same colour
(b) different colour

BKS 2019/20 Page 1

4. The Institute of Public health has discovered a new test for cancer. Experimentation has
shown that if a person has cancer, the probability of a positive test result is 0.80. If a person
does not have cancer, the probability of a positive test result is 0.06. Suppose that 35% of
a population has some kind of cancer.
(a) Construct a tree diagram to represent the above information.
(b) Find the probability that a person chosen at random
(i) has cancer and positive test result.
(ii) has positive test result.
(iii) has cancer or positive test result.
(iv) has cancer, given that the test result was negative.

5. The students at a certain university have to register subjects online. A survey has been
make to identify the type of internet connection used for registration. For 2018 intake, 35 %
of the students used public Wi-Fi, 40 % used personal broadband and the rest used
university internet cable. 75% students who use public Wi-Fi and 40 % of students who
used personal broadband failed to register online. However, 90% of the students who used
university internet cable were able to register successfully.
(a) Construct a tree diagram to represent the above information.
(b) Find the probability that the student used university cable if the student failed to register
online.
(c) If two students are randomly chosen from the population, find the probability that at
least one of them failed to register online.

BKS 2019/20 Page 2

Unit Matematik

Kolej Matrikulasi Johor
Kementerian Pendidikan Malaysia

JOM-DO-MATH(JDM)
Chapter 8 Probability ( Set 3 )

1. A survey on 1000 adults was done to find out whether or not they have e-mail account. The

following table summarises the responses.

Male Yes No
Female 500 100
250 150

If an adult is selected at random from these 1000 adults, find the probability that the adult
(a) has an e-mail account.
(b) is a female
(c) has no e-mail account given that the adult is a male
(d) is a female given that the adult has an e-mail account.

2. Samples of 500 teachers were ask whether they have ever shopped on the internet or not.
The following table give a two-way classification of the responses.

Male Have Shopped Have Never Shopped
Female 225 75
150 50

If one teacher is selected randomly from these 500 teachers, find the probability that the
teacher

(a) have never shopped on the internet.
(b) is a male
(c) has shopped on the internet given that the teacher is a female.
(d) is a male given that he has never shopped on the internet.

BKS 2019/20 Page 1

3. The table below shows the number of male and female students taking part in four types

of sports at a college.

Squash Badminton Archery Tennis

Male 7 x 5 23
120 24 120

Female 1 1 1 y

12 30 8

(a) Given that the probability that a student taking part in a sport is male is 7 . Find the
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values of x and y.
(b) One of the students is chosen randomly. Find the probability that the student is

(i) A female or playing tennis.
(ii) A male if he also takes archery
(iii) A female who plays squash or a male who plays badminton.

4. In a survey conducted towards 500 respondents, 45% of them are married. One fifth of the
respondents are single male. There are equal numbers of males and females respondents
involved in the survey.
(a) Conducted an appropriate contingency table.
(b) If a respondents is chosen at random, find the probability that
(i) the respondent is married females.
(ii) the respondent is a male, if it is know that he is married.
(iii) the respondent is married, if it is know that the respondent is a male.

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5. A survey was carried out on 200 teenagers who owned either Nokia, Samsung or Motorola
hand phone. 90 of the teenagers were male. Out of the 100 teenagers that owned Nokia
hand phone, 50 were female. 30 males owned Samsung hand phones and 40 female owned
Motorola hand phones. If a teenager who owned a hand phone is selected randomly, find
the probability that the teenager
(a) Is a male who owned Nokia hand phone.
(b) Owned Nokia or Samsung hand phone.
(c) Is a female or owned a Motorola hand phone.

BKS 2019/20 Page 3

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