Two cards are drawn successively without replacement from a standard deck of 52 cards. What is the probability that the first card is a spade and the second card is a heart?

Step-by-step solution

1. Step 1: Compute the probability that the first card drawn is a spade: $\frac{13}{52}=\frac{1}{4}$.
2. Step 2: After drawing a spade, 51 cards remain, of which 13 are hearts.
3. Step 3: Compute the conditional probability that the second card is a heart: $\frac{13}{51}$.
4. Step 4: Multiply the probabilities of the two independent steps: $\frac{1}{4}\times \frac{13}{51}=\frac{13}{204}\approx 0.0377$.
5. Step 5: State the final probability as $0.0377$ (rounded to four decimal places).

Concept tested: Conditional probability without replacement

Published 12 September 2026 · Last updated 16 September 2026 · How this solution was prepared and checked