Subjects probability

Conditional Probability E028B4

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1. **State the problem:** We need to find the conditional probability $P(D|C)$, which is the probability of event $D$ occurring given that event $C$ has occurred. 2. **Formula:** The conditional probability is given by $$P(D|C) = \frac{P(D \cap C)}{P(C)}$$ where $P(D \cap C)$ is the probability that both $D$ and $C$ occur, and $P(C)$ is the probability that $C$ occurs. 3. **Identify values from the table:** From the table, - $P(D \cap C) = 0.05$ - $P(C) = 0.30$ 4. **Calculate $P(D|C)$:** $$P(D|C) = \frac{0.05}{0.30}$$ 5. **Simplify the fraction:** $$P(D|C) = \frac{\cancel{0.05}}{\cancel{0.30}} = \frac{1}{6} \approx 0.1667$$ 6. **Round to two decimal places:** $$P(D|C) \approx 0.17$$ **Final answer:** $$\boxed{0.17}$$