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1. Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the
probability that the ticket drawn has a number which is a multiple of 3 or 5?
1
2
A.
B.

2

5

8
9
C.
D.

15

20

Explanation:
Here, S = {1, 2, 3, 4, ...., 19, 20}.
Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}.
n(E) 9
P(E) =
= .
n(S) 20

2. A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the
probability that none of the balls drawn is blue?
10
11
A.
B.

21

21

2
5
C.
D.

7

7

Explanation:
Total number of balls = (2 + 3 + 2) = 7.
Let S be the sample space.
Then, n(S) = Number of ways of drawing 2 balls out of 7
= 7C

2
(7 x 6)
=

(2 x 1)

= 21.

Let E = Event of drawing 2 balls, none of which is blue.
n(E) = Number of ways of drawing 2 balls out of (2 + 3) balls.
= 5C

2
= (5 x 4)

(2 x 1)

= 10.

n(E) 10
P(E) =
= .
n(S) 21

3. In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the
probability that it is neither red nor green?
1
3
A.
B.

3

4

7
8
C.
D.

19

21

9
E. 21

Explanation:
Total number of balls = (8 + 7 + 6) = 21.
Let E = event that the ball drawn is neither red nor green
= event that the ball drawn is blue.

n(E) = 7.
n(E) 7 1
P(E) =
= = .
n(S) 21 3

4. What is the probability of getting a sum 9 from two throws of a dice?
1
1
A.
B.

6

8

1
1
C.
D.

9

12

Explanation:
In two throws of a die, n(S) = (6 x 6) = 36.
Let E = event of getting a sum ={(3, 6), (4, 5), (5, 4), (6, 3)}.
n(E) 4 1
P(E) =
= = .
n(S) 36 9

5. Three unbiased coins are tossed. What is the probability of getting at most two heads?
3
1
A.
B.

4

4

3
7
C.
D.

8

8

Explanation:
Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}
Let E = event of getting at most two heads.
Then E = {TTT, TTH, THT, HTT, THH, HTH, HHT}.
n(E) 7
P(E) =
= .
n(S) 8

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