1. **Problem Statement:** Find the probability that the first card drawn is red and the second card drawn is black from a standard 52-card deck. 2. **Key Information:** - Total cards: 52 - Red cards: 26 (hearts and diamonds) - Black cards: 26 (clubs and spades) 3. **Part (A) Without Replacement:** - The first card is red: Probability = $\frac{26}{52} = \frac{1}{2}$ - After drawing one red card, cards left = 51 - Black cards remain 26 (unchanged) - Probability second card is black = $\frac{26}{51}$ 4. **Combined Probability (without replacement):** $$ P = \frac{26}{52} \times \frac{26}{51} = \frac{1}{2} \times \frac{26}{51} = \frac{26}{102} = \frac{13}{51} \approx 0.2549 $$ 5. **Part (B) With Replacement:** - The first card is red: Probability = $\frac{26}{52} = \frac{1}{2}$ - Since the card is replaced, the deck is back to 52 cards - Probability second card is black = $\frac{26}{52} = \frac{1}{2}$ 6. **Combined Probability (with replacement):** $$ P = \frac{26}{52} \times \frac{26}{52} = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} = 0.25 $$ **Final answers:** - (A) Without replacement: $0.2549$ - (B) With replacement: $0.25$