# 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

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