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

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: 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: 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: 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: Option B

Explanation:

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

Number of white balls = 8.

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


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