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:** - There are 52 cards total. - Hearts are one of the four suits, with 13 cards. - Red cards are hearts and diamonds, so there are $13 + 13 = 26$ red cards. 4. **Calculate $P(A \cap B)$:** Since all hearts are red, $A \cap B$ is just the event "card is a heart," so $$P(A \cap B) = \frac{13}{52} = \frac{1}{4}$$ 5. **Calculate $P(B)$:** $$P(B) = \frac{26}{52} = \frac{1}{2}$$ 6. **Apply the conditional probability formula:** $$P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{\frac{1}{4}}{\frac{1}{2}}$$ 7. **Simplify the fraction:** $$P(A|B) = \frac{1}{4} \times \frac{2}{1} = \frac{2}{4} = \frac{1}{2}$$ **Final answer:** The probability that the card is a heart given that it is red is $\boxed{\frac{1}{2}}$.