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(S)=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(B)=12
∴ 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}