TITLE: Probability that a card drawn is King on condition that the card is a Heart
QUESTION [4 upvotes]: 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?

REPLY [1 votes]: We want to work out $P(king|heart)$. 
$P(heart)=1/4$
$P(king \& heart)=1/52$
Conditional probability formula: $P(A|B)=P(A \& B)/P(B)$. 
So substituting into this formula we get:
$P(king | heart) = P(king \& heart) / P(heart) = (1/52)/(1/4) = 4/52 = 1/13$ as required.
So yes, you are correct.
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