1. **Problem Statement:** Find the probability that both cards drawn without replacement from a standard deck of 52 cards are black. 2. **Understanding the problem:** - There are 52 cards total. - Half of them (26) are black. - Drawing without replacement means the first card is removed before drawing the second. 3. **Formula for dependent events:** For dependent events A and B, the probability of both occurring is: $$P(A \text{ and } B) = P(A) \times P(B|A)$$ where $P(B|A)$ is the probability of B given A has occurred. 4. **Calculate $P(\text{first card black})$:** $$P(\text{first black}) = \frac{26}{52} = \frac{1}{2}$$ 5. **Calculate $P(\text{second card black} | \text{first card black})$:** After drawing one black card, there are 25 black cards left and 51 cards total: $$P(\text{second black} | \text{first black}) = \frac{25}{51}$$ 6. **Calculate overall probability:** $$P(\text{both black}) = \frac{26}{52} \times \frac{25}{51} = \frac{1}{2} \times \frac{25}{51} = \frac{25}{102} \approx 0.245$$ 7. **Intermediate step showing cancellation:** $$P = \frac{\cancel{26}}{\cancel{52}} \times \frac{25}{51} = \frac{1}{2} \times \frac{25}{51} = \frac{25}{102}$$ **Final answer:** $$\boxed{\frac{25}{102} \approx 0.245}$$