Two cards are drawn together from a pack of 52 cards. The probability that one is a spade and one is a heart… · ABC26GN5354
Subject: General Aptitude · Chapter: Probability
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)$\frac{13}{102}$
Answer
Answer (as printed): D
Explanation
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. $\therefore \quad n(E)=$ number of ways of choosing 1 spade out of 13 and 1 heart out of 13 $=\left({ }^{13} \mathrm{C}_{1} \times{ }^{13} \mathrm{C}_{1}\right)=(13 \times 13)=169$. $$\therefore \quad P(E)=\frac{n(E)}{n(S)}=\frac{169}{1326}=\frac{13}{102} .$$
Explanation as extracted from the printed page; notation may be imperfect.