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Probability - General Aptitude

Q1:

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

ANS:D -

13
102

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