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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

\begin{aligned} n (S) =^{52} C_{2} = \frac{52 \times 51}{2 \times 1} \\ = 1326 \end{aligned}

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

\begin{aligned} =^{13} C_{1} \times^{13} C_{1} \\ = 13 \times 13 \\ = 169 \\ ∴ P (E) = \frac{n (E)}{n (S)} = \frac{169}{1326} = \frac{13}{102} \end{aligned}

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