1. One member is chosen randomly from a soccer team with 12 members to be the captain. Terry is one
of the members, what is the probability of choosing Terry?
P(choosing Terry)

2. An integer between 0 and 15 is randomly chosen. Find the probability that this integer satisfies each
of the following conditions.
(a) An odd number
[ Analysis: There are
integers, of which
integers are odd numbers. ]
P(odd number)

(
(
)
)

6.1
 2010 Chung Tai Educational Press. All rights reserved.
(b) A multiple of 5
[ Analysis: There are
integers, of which
integers are multiples of 5. ]
P(multiple of 5)


3. A letter is randomly selected from the word ‘PEOPLE’. Find the probabilities of the following events
happening.
(a) The letter selected is ‘P’.
[ Analysis: There are
letters in the word, of which
letters are ‘P’. ]
P(‘P’)


(b) The letter selected is not ‘E’.
[ Analysis: There are
letters in the word, of which
P(not ‘E’)


6.2
 2010 Chung Tai Educational Press. All rights reserved.
letters are not ‘E’. ]
4. There are 5 red ballpoint pens, 6 black ballpoint pens and 4 green ballpoint pens in a box. If
a ballpoint pen is drawn at random from the box, find the probabilities of the following events
happening.
(a) A red ballpoint pen or a green ballpoint pen is drawn.
[ Analysis: There are
ballpoint pens in the box, of which
ballpoint pens are red or green. ]
P(red ballpoint pen or green ballpoint pen)


(b) The ballpoint pen drawn is not red.
[ Analysis: There are
ballpoint pens in the box, of which
ballpoint pens are not red. ]
P(not a red ballpoint pen)


6.3
 2010 Chung Tai Educational Press. All rights reserved.
5. There are 30 chocolates (C ) and x marshmallows (M ) in a candy box. If a candy is chosen randomly
3
from the candy box, the probability of choosing a marshmallow is .
8
(a) Find the probability of choosing a chocolate.


1
P(C ) 



(b) Find the value of x.

P(C ) 


(
(
6.4
 2010 Chung Tai Educational Press. All rights reserved.
)
)
1. The results of rolling a dice 250 times are as follows:
Number
1
2
3
4
5
6
Frequency
35
47
53
40
48
27
(a) Find the experimental probability that the number is 1.
Experimental probability that the number is 1


(b) Find the experimental probability that the number is a multiple of 3.
Experimental probability that the number is a multiple of 3



6.5
 2010 Chung Tai Educational Press. All rights reserved.
2. The table below shows the number of late arrivals of S3A in April.
Number of late arrivals
0
1
2
3
4
Frequency
18
10
5
2
1
(a) Find the number of students in S3A.
Number of students






(b) If a student is chosen randomly from S3, estimate the probabilities of the following events happening.
(i) The student was not late for school in April.
Probability that the student was not late for school in April


6.6
 2010 Chung Tai Educational Press. All rights reserved.
(ii) The number of late arrivals of the student in April is more than 2.
Probability that the number of late arrivals of the student in April is more than 2



3. The figure shows the number of days of absence among the 15 employees of the human resources
department in a company last month.
Absence records of the employees of
the human resources department last month
Frequency
10
8
6
4
2
0
1
2
3
Number of days of absence
6.7
 2010 Chung Tai Educational Press. All rights reserved.
(a) Find the relative frequency of the employees of the human resources department without any
absence records last month.
The relative frequency of the employees of the human resources department without any absence
records last month

(
(
)
)

(b) There are 2 500 employees in the company, estimate the number of employees in the company
without any absence records last month.
The number of employees in the company without any absence records last month



6.8
 2010 Chung Tai Educational Press. All rights reserved.
1. 2 fair dice are rolled.
(a) List the sample space in the table below.
II
I
1
2
3
4
5
6
1
2
3
4
5
6
(b) Find the probabilities of the following events happening.
(i) The sum of the numbers obtained from the two dice equals 7.
Required probability

(
(
)
)

6.9
 2010 Chung Tai Educational Press. All rights reserved.
(ii) The sum of the numbers obtained from the two dice is greater than 7.
Required probability


2. There are 2 yellow balls (Y1 , Y2 ) and 3 white balls (W1 , W2 , W3 ) in a bag. A ball is drawn at random
from the bag, and is put back into the bag before drawing a ball at random again.
(a) List the sample space in the table below.
Second Ball
Y1
Y2
W1
First Ball
Y1
Y2
W1
W2
W3
(b) Find the probability that a white ball is drawn twice.
Required probability

6.10
 2010 Chung Tai Educational Press. All rights reserved.
W2
W3
3. There are 4 red balls (R1 , R 2 , R 3 , R 4 ) and 3 black balls (B1 , B2 , B3 ) in a bag. 2 balls are drawn at
the same time at random.
(a) List the sample space in the following table, and find the total number of possible outcomes.
II
I
R1
R2
R3
R4
B1
B2
B3
R1
R2
R3
R4
B1
B2
B3
The total number of possible outcomes

(b) Find the probability that at least one red ball is drawn.
Required probability


6.11
 2010 Chung Tai Educational Press. All rights reserved.
4. A fair coin is tossed three times.
(a) Represent a ‘head’ and a ‘tail’ by ‘H’ and ‘T’ respectively. List the sample space.
We can use a tree diagram to represent all the possible outcomes (i.e. sample space).
First toss
Second toss
Third toss
Outcome
From the figure, the sample space is
.
(b) Find the probability of getting at most one ‘head’.
Required probability


6.12
 2010 Chung Tai Educational Press. All rights reserved.
1. The following figures are dartboards formed by a number of congruent triangles. If a dart hits a point
at random on each of the following dartboards without hitting the boundaries, find the probability
that it hits the shaded region.
(a)
Required probability

(
(
)
)

(b)
Required probability

6.13
 2010 Chung Tai Educational Press. All rights reserved.
(c)
Required probability


2. The figure shows a circular dartboard. The shaded region on the dartboard is a square. The radius of
the circle and the length of sides of the square are 6 cm and 4 cm respectively. Now, a dart hits
a point at random on the dartboard without hitting the boundaries, find the probability that it hits the
shaded region. (Express your answer in terms of .)
4 cm
6 cm
Total area
 

cm2
cm2
6.14
 2010 Chung Tai Educational Press. All rights reserved.
Area of the shaded region

cm2

cm2
 P(hitting the shaded region)

(
(
)
)

3. During the rush hour, a train arrives at a railway station every 2 minutes and stays there for
20 seconds. Raymond arrives at the platform of the station during the rush hour withou t knowing the
timetable of trains. Find the probability that a train stays in the station when Raymond arrives.
Length of time between the arrivals of two trains at the station

Length of time for each train to stay in the station

 Required probability

(
(
)
)

6.15
 2010 Chung Tai Educational Press. All rights reserved.
4. There are 5 cards of the same size numbered 1, 3, 8, 8 and 10 in a bag. A card is drawn from the bag
at random.
(a) Find the probability of drawing each number on the card.
P(1) 
P(3) 
P(8) 
P(10) 
(b) Find the expected value of the number on the card drawn.
Expected value of the number on the card drawn









6.16
 2010 Chung Tai Educational Press. All rights reserved.
