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 630 customers.
if one of these customers is selected at random, determine the probability of a sale, given that the passive approach was used.
the probability of a sale, given that the passive approach was used, is
(type an integer or a simplified fraction.)

Explanation:

Step1: Recall conditional probability formula

The formula for conditional probability is \(P(A|B)=\frac{P(A\cap B)}{P(B)}\). In the context of the table, if \(A\) is "sale" and \(B\) is "passive approach", then \(P(A\cap B)\) is the number of sales with passive approach, and \(P(B)\) is the total number of passive - approach cases.

Step2: Identify values from the table

From the table, the number of sales with a passive approach (\(A\cap B\)) is \(210\), and the total number of passive - approach cases (\(B\)) is \(280\).

Step3: Calculate the probability

Using the formula \(P(A|B)=\frac{210}{280}\). Simplify the fraction: \(\frac{210\div70}{280\div70}=\frac{3}{4}\)

Answer:

\(\frac{3}{4}\)