1. **State the problem:** We want to find the conditional probability that a card drawn from a standard 52-card deck is a heart, given that the card is red. 2. **Recall the formula for conditional probability:** $$P(A|B) = \frac{P(A \cap B)}{P(B)}$$ where $A$ is the event "card is a heart" and $B$ is the event "card is red". 3. **Identify the events:** - Total cards: 52 - Red cards: 26 (hearts and diamonds) - Hearts: 13 4. **Calculate $P(A \cap B)$:** Since all hearts are red, $A \cap B$ is just the event "card is a heart," so $$P(A \cap B) = \frac{13}{52}$$ 5. **Calculate $P(B)$:** Probability the card is red is $$P(B) = \frac{26}{52}$$ 6. **Apply the conditional probability formula:** $$P(A|B) = \frac{\frac{13}{52}}{\frac{26}{52}}$$ 7. **Simplify the fraction:** $$P(A|B) = \frac{13}{52} \times \frac{52}{26} = \frac{13}{\cancel{52}} \times \frac{\cancel{52}}{26} = \frac{13}{26}$$ 8. **Simplify further:** $$P(A|B) = \frac{13}{26} = \frac{1}{2}$$ **Final answer:** The conditional probability that the card is a heart given that it is red is $\frac{1}{2}$.