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# Two cards are drawn from a well - shuffled pack of 52 cards without replacement. What is the probability that one is a red queen and the other is a king of black colour.

Toolbox:
• If A and B are independant events, $P(A\cap\;B)=P(A)\;P(B)$
Step 1:
Let $P(R_1)$ be the probability of getting a red queen in the I draw =$\large\frac{2}{52}$
Let $P(K_2)$ be the probability of getting a king of black in the II draw $=\large\frac{2}{51}$
Let $P(R_2)$ be the probability of getting a red queen in the II draw $=\large\frac{2}{51}$
Let $P(K_1)$ be the probability of getting a black king in the I draw $=\large\frac{2}{52}$
Step 2:
Required probability is $P(R_1).P(\large\frac{K_2}{R_1})$$+P(K_1).P(\large\frac{R_2}{K_1})$
$\Rightarrow \large\frac{2}{52}\times \frac{2}{51}+\frac{2}{52}+\frac{2}{51}$
$\Rightarrow \large\frac{2}{663}$