Question

Two cards are drawn successively from a well shuffled pack of $52$ cards. Find the probability that one is a red card and the other is a queen.

• A. $\frac{103}{1326}$
• B. $\frac{101}{1326}$
• C. $\frac{101}{1426}$
• D. $\frac{103}{1426}$

Answer 1

Answer: (B)

Here we assume that drawing two queen (whether both red or one red and one black) is allowed. Now one red card and one queen can be drawn in following ways :
(i) $P$(red queen, red queen) $=\frac{2}{52}\cdot \frac{1}{51}$
(ii) $P$(red non-queen, red queen) $=\frac{24}{52}\cdot \frac{2}{51}$
(iii) $P$(red queen, red non-queen) $=\frac{2}{52}\cdot \frac{24}{51}$
(iv) $P$(red card, black queen) $=\frac{26}{52}\cdot \frac{2}{51}$
(v) $P$(black queen, red card) $=\frac{2}{52}\cdot \frac{26}{51}$
Required probability
$=\frac{2}{52\cdot 51}+\frac{48}{52\cdot 51}+\frac{48}{52\cdot 51}+\frac{52}{52\cdot 51}+\frac{52}{52\cdot 51}$
$=\frac{101}{1326}$