Question

the table shows the result of a restaurant survey. find the probability the service was good, given that the meal was lunch. the probability the service was good, given that the meal was lunch, is
(type an integer or a simplified fraction.)

Explanation:

Step1: Recall the formula for conditional probability

The formula for conditional probability is \(P(A|B)=\frac{P(A\cap B)}{P(B)}\). In the context of this problem, if \(A\) is the event that the service was good and \(B\) is the event that the meal was lunch, then \(P(A|B)=\frac{\text{Number of lunch - good service meals}}{\text{Number of lunch meals}}\).

Step2: Identify the relevant values from the table

From the table, the number of lunch - good service meals (\(n(A\cap B)\)) is \(39\), and the number of lunch meals (\(n(B)\)) is \(88\).

Answer:

\(\frac{39}{88}\)