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

/ Aptitude, Probability / By
Question: 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