Tak Sun Secondary School
Marks
Form 3 Mathematics (Introduction to Probability)
Revision Exercise 2016-2017
Name : ___________________________
/50
Class : _________ No. :_______
Section A : Multiple Choices (3 marks each, 24 marks in Total)
Choose the most suitable answer and write down into the corresponding boxes.
Time Allowed: 35 minutes
1.
A
2.
C
3.
B
6.
B
7.
B
8.
A
4.
B
5.
D
1. A number is chosen randomly from the integers 1 to 40. Find the probability of getting a multiple
of 8.
A. 0.125
B. 0.25
C. 0.375
D. 0.5
2. A letter is chosen randomly from the letters of the word ‘MANDARIN’. What is the probability
that it is either an ‘M’ or ‘N’?
1
A.
2
1
B.
3
3
C.
8
4
D.
9
3. Two digits are chosen at random from the password 814718. Find the probability that the two
digits are different.
13
A.
18
13
B.
15
4
C.
5
2
D.
3
1
4.
A survey on the polling of the nominated student union committees A and B was conducted.
Some votes of male and female voters were recorded as follows:
Committee A Committee B
Number of male voters
76
53
Number of female voters
82
89
What is the experimental probability that a student voted for the nominated committee B?
5.
A.
53
142
B.
71
150
C.
79
150
D.
89
142
A bag contains 12 marbles, of which 4 are green. If a marble is drawn at random from the bag,
find the probability of not getting a green marble.
1
12
1
B.
4
1
C.
3
2
D.
3
A.
6.
At the entrance of a plaza, a shuttle bus comes in every 30 minutes and it waits 5 minutes at
the bus stop. If a customer does not know the timetable of the shuttle bus service, find the
probability that he can get on the bus without waiting.
1
A.
5
1
B.
6
1
C.
10
2
D.
15
2
7.
8.
Two fair dice are thrown. Find the probability that the number on a dice is twice the number on
another dice.
A.
1
9
B.
1
6
C.
1
4
D.
1
3
In a coin game, Charlie tosses two coins. If two tails are obtained, he will get $10. Otherwise, he
has to pay $4. What is his expected reward in the game for each turn?
A. –$0.5
B. $2.5
C. $3
D. $6
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Section B : Short Questions (26 marks in Total)
Please write all answers with steps in the spaces provided.
9. A number is randomly selected from the integers 1 to 40. What is the probability that the number
selected is
(a) a multiple of 4?
(b) not a multiple of 4?
(6 marks)
Total number of possible outcomes = 40
(a) 4, 8, 12, 16, 20, 24, 28, 32, 36 and 40 are multiples of 4.
 Number of favourable outcomes = 10

10
40
1

4
1A
P(a multiple of 4) 
1A
(b) Number of favourable outcomes = 40  10 = 30

1A
30
40
3

4
P(not a multiple of 4) 
1A
1M
1A
4
10.
A lucky draw is held in a shopping mall and the details are as follows: there is a bag containing 3
balls with a yellow dot, a red dot and a white dot respectively. A customer draws a ball at random
and puts it back into the bag after recording its colour. Then a ball is drawn again. If the colours of
two balls drawn are the same, a price will be given. Find the probability that the colours of two
balls drawn are the same. (Use a tree diagram to solve the problem.)
(6 marks)
Let Y stand for ball with a yellow dot, R stand for ball with a red dot and W stand for ball with a white
dot.
The tree diagram below shows all the possible outcomes of the balls drawn:
1st ball
2nd ball
Y
Y
R
W
……………………
……………………
……………………
YY
YR
YW
R
Y
R
W
……………………
……………………
……………………
RY
RR
RW
W
Y
R
W
……………………
……………………
……………………
WY
WR
WW
Outcome
1M+1A
1A
1A
Total number of possible outcomes = 9
Number of favourable outcomes = 3

3
9
1

3
P(same colour) 
1M
1A
5
11. A bag contains 12 black balls, 18 white balls, 13 red balls and 7 brown balls. If a ball is drawn at
random, find the probability that the ball drawn is
(a) not a black ball.
(b) neither a red ball nor a brown ball.
(7 marks)
Total number of possible outcomes = 12 + 18 + 13 + 7 = 50
(a) Balls which are not black: 18 white balls, 13 red balls and 7 brown balls
 Number of favourable outcomes = 18 + 13 + 7 = 38
38
 P(not a black ball) 
50
19

25
(b) Balls which are neither red nor brown: 12 black balls and 18 white balls
 Number of favourable outcomes = 12 + 18 = 30
30
 P(neither a red ball nor a brown ball) 
50
3

5
1A
1A
1M
1A
1M
1A
1A
___________________________________________________________________________________
12. An organization issues 50 000 lucky draw tickets. The prizes are as follows:
Prize item
Number of prizes
Prize
1st prize
1
$100 000
2nd prize
1
$50 000
3rd prize
3
$10 000
Consolation prize
5
$1 000
(a) Find the expected value of the prize of each of the lucky draw tickets.
(b) If Jacky buys a lucky draw ticket of $20, does he gain or suffer a loss on average? Explain
your answer.
(7 marks)
1
(a) P(1st prize) 
50 000
1
P(2nd prize) 
50 000
6
P(3rd prize) 
3
50 000
5
50 000
1

10 000
Expected value of the prize of each of the lucky draw tickets
1
1
3

 $100 000 
 50 000 
 10 000 

50 000
50 000
50 000

1 
1 000 

10 000 
 $(2  1  0.6  0.1)
 $3.7
P(Consolation prize) 
2A for all P(E)
1M+1A
1A
(b) Since the expected value of the prize of each of the lucky draw tickets is less than the price of the
ticket, he will suffer a loss on average.
1M+1A
___________________________________________________________________________________
End of Paper
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