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 (since no black card was drawn yet) - Probability second card is black = $\frac{26}{51}$ 4. **Calculate combined probability:** $$ P(\text{red then black}) = P(\text{red first}) \times P(\text{black second | red first}) = \frac{26}{52} \times \frac{26}{51} $$ 5. **Simplify:** $$ = \frac{1}{2} \times \frac{26}{51} = \frac{26}{102} = \frac{\cancel{26}}{\cancel{102}} \rightarrow \frac{13}{51} $$ 6. **Decimal form:** $$ \frac{13}{51} \approx 0.2549 $$ 7. **Answer for (A):** The probability without replacement is approximately **0.2549**. 8. **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 = $\frac{26}{52} = \frac{1}{2}$ 9. **Calculate combined probability:** $$ P(\text{red then black}) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} = 0.25 $$ 10. **Answer for (B):** The probability with replacement is **0.25**.