A box contains 10 cards: 4 hearts, 3 spades, 2 clubs and 1 diamond. Two cards are drawn successively without replacement. What is the probability that the first card is a heart and the second card is a club?

Step-by-step solution

1. First draw a heart: $P(\text{heart first})=\frac{4}{10}$.
2. After removing one heart, there remain 9 cards, including 2 clubs. So $P(\text{club second}\mid \text{heart first})=\frac{2}{9}$.
3. Multiply the conditional probabilities: $P(\text{heart then club})=\frac{4}{10}\times \frac{2}{9}=\frac{8}{90}=\frac{4}{45}$.
4. Thus the required probability is $\frac{4}{45}$.

Concept tested: Conditional probability in sequential events

Published 4 October 2026 · How this solution was prepared and checked