Question

Two cards are drawn without replacement from a well shuffled pack of 52 cards. Find the probability that one is a spade and other is a queen of red colour.

Answer 1

$S_i=$ getting a spade card in the ith draw ; $i=1,2$

$Q_i=$ getting a red queen in the ith draw ; $i=1,2$

Required probability = $P(S_1\cap Q_2)\cup (Q_1\cap S_2)$

$=P(S_1\cap Q_2)+P(Q_1\cap S_2)$

$=P\left(S_1\right)P\left(Q_2/S_1\right)+P\left(Q_1\right)P\left(S_2/Q_1\right)$

$=\frac{{{13}_C}_1}{{{52}_C}_1}\times \frac{{2_C}_1}{{{51}_C}_1}+\frac{{2_C}_1}{{{52}_C}_1}\times \frac{{{13}_C}_1}{{{51}_C}_1}$

$=2(\frac{13}{52}\times \frac{2}{51})=\frac{1}{51}$