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. $\frac{7}{102}$
• B. $\frac{9}{102}$
• C. $\frac{11}{102}$
• D. $\frac{13}{102}$

Answer 1

The correct option is D $\frac{13}{102}$

Let S be the sample space.

Then, $n\left(S\right){=}^{52}{C}_2=\frac{(52\times 51)}{2\times 1}=1326$

Let E = event of getting 1 spade and 1 heart.

$n\left(E\right)$ = number of ways of choosing 1 spade out of 13 and 1 heart out of 13

$={(}^{13}{C}_1{\times }^{13}{C}_1)=13\times 13=169$

Hence, the probability that one is a spade and one is a heart, is:

$P\left(E\right)=\frac{n\left(E\right)}{N\left(S\right)}=\frac{169}{1326}=\frac{13}{102}$