# probability aptitude questions

**11.**

A card is drawn from a pack of 52 cards. The probability of getting a queen of club or a king of heart is:

A.

1

13

B.

2

13

C.

1

26

D.

1

52

Answer & Explanation

Answer: Option C

Explanation:

Here, n(S) = 52.

Let E = event of getting a queen of club or a king of heart.

Then, n(E) = 2.

P(E) = n(E) = 2 = 1 .

n(S) 52 26

12.

A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is:

A.

1

22

B.

3

22

C.

2

91

D.

2

77

Answer & Explanation

Answer: Option C

Explanation:

Let S be the sample space.

Then, n(S) = number of ways of drawing 3 balls out of 15

= 15C3

= (15 x 14 x 13)

(3 x 2 x 1)

= 455.

Let E = event of getting all the 3 red balls.

n(E) = 5C3 = 5C2 = (5 x 4) = 10.

(2 x 1)

P(E) = n(E) = 10 = 2 .

n(S) 455 91

13.

Two cards are drawn together from a pack of 52 cards. The probability that one is a spade and one is a heart, is:

A.

3

20

B.

29

34

C.

47

100

D.

13

102

Answer & Explanation

Answer: Option D

Explanation:

Let S be the sample space.

Then, n(S) = 52C2 = (52 x 51) = 1326.

(2 x 1)

Let E = event of getting 1 spade and 1 heart.

n(E) = number of ways of choosing 1 spade out of 13 and 1 heart out of 13

= (13C1 x 13C1)

= (13 x 13)

= 169.

P(E) = n(E) = 169 = 13 .

n(S) 1326 102

14.

One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is a face card (Jack, Queen and King only)?

A.

1

13

B.

3

13

C.

1

4

D.

9

52

Answer & Explanation

Answer: Option B

Explanation:

Clearly, there are 52 cards, out of which there are 12 face cards.

P (getting a face card) = 12 = 3 .

52 13

15.

A bag contains 6 black and 8 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?

A.

3

4

B.

4

7

C.

1

8

D.

3

7

Answer & Explanation

Answer: Option B

Explanation:

Let number of balls = (6 + 8) = 14.

Number of white balls = 8.

**P (drawing a white ball) = 8 = 4 .
14 7**