From a standard deck of 52 cards, what is the probability that a randomly drawn card is a King, on condition that the card drawn is a Heart?
I used the conditional probability formula and got:
Probability that the card is a King AND a Heart: $\frac{1}{52}$
Probability that the card is a Heart: $\frac{13}{52}$
So: $\frac{\frac{1}{52}}{\frac{13}{52}} = \frac{1}{13}$.
Is this correct?
Best Answer
Yes. There are thirteen hearts, and only one of them is a king.
$$\Pr(K \mid \heartsuit) = \frac{\Pr(K \cap \heartsuit)}{\Pr(\heartsuit)} = \frac{^1\!/_{52}}{^{13}\!/_{52}}=\frac{1}{13}$$