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1. Two cards are drawn from a pack of well shuffled cards. Find the probability that one is a club and other in King.

A. $\frac{1}{13}$

B. $\frac{4}{13}$

C. $\frac{1}{52}$

D. $\frac{1}{26}$

Solution:

Let X be the event that cards are in a club which is not king and other is the king of club.
Let Y be the event that one is any club card and other is a non-club king.
Hence, required probability:

\begin{aligned} = P (A) + P (B) \\ = \frac{^{12} C_{1} \times^{1} C_{1}}{^{52} C_{2}} + \frac{^{13} C_{1} \times^{3} C_{1}}{^{52} C_{2}} \\ = (\frac{2 \times (12 \times 1)}{52 \times 51}) + (\frac{2 (13 \times 3)}{52 \times 51}) \\ = (\frac{24 + 78}{52 \times 51}) \\ = \frac{1}{26} \end{aligned}

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