One card is drawn from a standard deck of cards. What is the probability that it is a queen if it is known to be a face card?
Number of elements in sample space $S = n \left(S\right) = 52$
Let $A$ be the event of drawing a queen.
Let $B$ be the event of drawing a face card.
Number of elements in $B = n \left(B\right) = 12$
$\therefore \;$ $P \left(B\right) = \dfrac{n \left(B\right)}{n \left(S\right)} = \dfrac{12}{52}$
$\left(A \cap B\right) = $ event that the face card is a queen
$\because \;$ There are $4$ queen cards, $n \left(A \cap B\right) = 4$
$\therefore \;$ $P \left(A \cap B\right) = \dfrac{n \left(A \cap B\right)}{n \left(S\right)} = \dfrac{4}{52}$
$\therefore \;$ Probability of drawing a queen if the card selected is a face card
$= P \left(A | B\right) = \dfrac{P \left(A \cap B\right)}{P \left(B\right)} = \dfrac{4/52}{12/52} = \dfrac{4}{12} = \dfrac{1}{3}$