# Aptitude - Probability

### Exercise :: Probability - General 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

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

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

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

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

Explanation:

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

Number of white balls = 8.

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