Question: Compute the probability P(D|C) using P(DnC) P(C) A B C Totals D 0.30 0.15 0.10 0.55 E 0.10 0.15…

Compute the probability P(D|C) using P(DnC) P(C) A B C Totals D 0.30 0.15 0.10 0.55 E 0.10 0.15 0.20 0.45 Totals 0.40 0.30 0.30 1.00 and the appropriate table values. P(D|C) = (Round to two decimal places.)

Solution

To compute \( P(D|C) \), we use the formula: \[ P(D|C) = \frac{P(D \cap C)}{P(C)} \] From the table, we find: 1. \( P(D \cap C) \) is the probability of both D and C occurring together, which is given as 0.10. 2. \( P(C) \) is the total probability of C, which is the sum of all probabilities in column C: 0.10 + 0.20 = 0.30. Now, substitute these values into the formula: \[ P(D|C) = \frac{0.10}{0.30} \] Simplify the fraction: \[ P(D|C) = \frac{1}{3} \approx 0.33 \] Thus, \( P(D|C) = 0.33 \) rounded to two decimal places.