Question

Two cards are drawn from the standard deck of 52 playing cards without replacement. Find the probability of getting first card as queen and second as an ace.

• A. $\frac{1}{169}$
• B. $\frac{4}{663}$
• C. $\frac{1}{13}$
• D. $\frac{2}{13}$

Answer 1

The correct option is B $\frac{4}{663}$

Let A be the event of drawing first card as queen.
Let B be the event of drawing second card as ace.
Clearly, the two events are dependent.
$So,P\left(A\right)=\frac{4}{52}=\frac{1}{13}$
and $P\left(B\right)=\frac{4}{51}$

$ThenP\left(A\cap B\right)=P\left(A\right).P\left(B\right)=\frac{1}{13}\times \frac{4}{51}=\frac{4}{663}$