Question: Compute the probability P(D|C) using P(D|C) = P(DnC) / P(C) and the appropriate table values…

Compute the probability P(D|C) using P(D|C) = P(DnC) / P(C) and the appropriate table values. P(D|C) = (Round to two decimal places.)

Solution

To compute the probability \( P(D \mid C) \) using the formula given: \[ P(D \mid C) = \frac{P(D \cap C)}{P(C)} \] First, find \( P(D \cap C) \) from the table. This is the intersection of event \( D \) and \( C \). From the table: \[ P(D \cap C) = 0.10 \] Next, find \( P(C) \), which is the total probability of \( C \). From the table: \[ P(C) = 0.30 \] Now, substitute these values into the formula: \[ P(D \mid C) = \frac{0.10}{0.30} \] Calculate the result: \[ P(D \mid C) = 0.3333 \] Rounded to two decimal places: \[ P(D \mid C) = 0.33 \]