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1. 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. $\frac{3}{20}$

B. $\frac{29}{34}$

C. $\frac{47}{100}$

D. $\frac{13}{102}$

Solution:

Let S be the sample space.
Then, n(S) =

^{52} C_{2}

= \frac{(52 \times 51)}{(2 \times 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

= (^{13} C_{1} \times^{13} C_{1})

= (13 × 13) = 169

∴ P (E) = \frac{n (E)}{n (S)} = \frac{169}{1326} = \frac{13}{102}

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