Question

Two cards are drawn at random from a well shuffled pack of 52 playing cards. If one is found to be a king card, the probability that the other card is also king is

• A. $\frac{3}{13}$
• B. $\frac{32}{33}$
• C. $\frac{1}{33}$
• D. $\frac{2}{33}$

Answer 1

Answer: (C)

$\frac{1}{33}$

There are 2 possibilities:
(i) Both cards are kings: ${}^4{C}_2=6$
(ii) One card is a king and the other is not a king: ${}_1^{4}C{\ast }_1^{48}C=192$
Therefore, probability $=\frac{6}{6+192}=\frac{6}{198}=\frac{1}{33}$