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?
A.
1
2
B.
2
5
C.
8
15
D.
9
20
Answer & Explanation
Answer: Option D
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}.
P(E) = n(E) = 9 .
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?
A.
10
21
B.
11
21
C.
2
7
D.
5
7
Answer & Explanation
Answer: Option A
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
= 7C2 `
= (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.
= 5C2
= (5 x 4)
(2 x 1)
= 10.
P(E) = n(E) = 10 .
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?
A.
1
3
B.
3
4
C.
7
19
D.
8
21
E.
9
21
Answer & Explanation
Answer: Option A
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.
P(E) = n(E) = 7 = 1 .
n(S) 21 3
4.
What is the probability of getting a sum 9 from two throws of a dice?
A.
1
6
B.
1
8
C.
1
9
D.
1
12
Answer & Explanation
Answer: Option C
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)}.
P(E) = n(E) = 4 = 1 .
n(S) 36 9
5.
Three unbiased coins are tossed. What is the probability of getting at most two heads?
A.
3
4
B.
1
4
C.
3
8
D.
7
8
Answer & Explanation
Answer: Option D
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}.
P(E) = n(E) = 7 .
n(S) 8