Question

sales representatives at a car dealership were split into two groups. one group used an aggressive approach to sell a customer a new automobile. the other group used a passive approach. the following table summarizes the records for 695 customers.
if one of these customers is selected at random, determine the probability of a sale, given that the aggressive approach was used.
the probability of a sale, given that the aggressive approach was used, 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 a contingency - table, if \(A\) is the event of a sale and \(B\) is the event of an aggressive approach, then \(P(A|B)=\frac{\text{Number of sales with aggressive approach}}{\text{Total number of aggressive approaches}}\).

Step2: Identify the relevant values from the table

From the table, the number of sales with an aggressive approach (\(n(A\cap B)\)) is \(115\), and the total number of aggressive approaches (\(n(B)\)) is \(380\).

Step3: Calculate the probability

Using the formula \(P(A|B)=\frac{n(A\cap B)}{n(B)}\), we substitute \(n(A\cap B) = 115\) and \(n(B)=380\). So \(P(A|B)=\frac{115}{380}\). Simplify the fraction:

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Answer:

\(\frac{23}{76}\)