Statistics · Question of the Day

Statistics Question of the Day

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Friday, October 9, 2026

A card is drawn at random from a standard 52-card deck. Event $A$ is "the card is a heart," and event $B$ is "the card is a face card (J, Q, or K)." Based on the information given that $P(A\cap B)=\frac{3}{52}$ and $P(B)=\frac{12}{52}$ , what is $P(A\mid B)$ ? Give your answer as a simplified fraction.

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Question of the Day

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$\frac{4}{13}$
$\frac{3}{12}$
$\frac{1}{4}$ (correct answer)
$\frac{3}{52}$

Explanation: We need to find P(A|B), the probability a card is a heart given it's a face card. The conditional probability P(A|B) means "among face cards, what fraction are hearts?" We have P(B) = 12/52 (there are 12 face cards total) and P(A∩B) = 3/52 (there are 3 cards that are both hearts and face cards: J♥, Q♥, K♥). Using P(A|B) = P(A∩B)/P(B) = (3/52)/(12/52) = 3/12 = 1/4. This makes sense: of the 12 face cards, 3 are hearts, giving us 1/4. A common mistake is forgetting to divide the fractions properly or using 52 as the denominator after conditioning. Remember that conditioning restricts our sample space to just the face cards.