Two cards are drawn one after the other, without replacement, from a well-shuffled pack of 52. What is the probability that the first card is a heart and the second an ace?

\frac{1}{68}

Correct answerYour answer

\frac{4}{221}

Correct answerYour answer

\frac{1}{52}

Correct answerYour answer

\frac{1}{51}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

Split on the first card. The ace of hearts first: $\frac{1}{52} \times \frac{3}{51}$ ; another heart first: $\frac{12}{52} \times \frac{4}{51}$ .
$\frac{3 + 48}{2652} = \frac{51}{2652} = \frac{1}{52}$ .

Worth noting

$\frac{1}{51} = \frac{13}{52} \times \frac{4}{51}$ leaves all 4 aces in the pack, but the first heart may have been the ace of hearts.

Ten questions from Conditional Probability & Bayes' Theorem, at your own pace.

Explanation