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

Correct Answer: Option D

Let S be the sample space.

Then, n(S) = \(52C_2\) =(52 x 51)/(2 x 1) = 1326.

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

= \(13C_1\times13C_1\)

= 169.

P(E) = n(E)/n(S) = 169/1326 = 13/102.