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Aptitude - Probability

Exercise : Probability - General Questions
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
2
5
8
15
9
20
Answer: Option
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?
10
21
11
21
2
7
5
7
Answer: Option
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?
1
3
3
4
7
19
8
21
9
21
Answer: Option
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?
1
6
1
8
1
9
1
12
Answer: Option
Explanation:

In two throws of a dice, 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?
3
4
1
4
3
8
7
8
Answer: Option
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

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