Question

2025 - 26 bcp5 geometry: concepts and connections
probability and statistics
the manager of a grocery store reports that there is a 12 percent chance that a customer buys apples during a shopping trip, a 5 percent chance that a customer buy apples and carrots, and a 17 percent chance that a customer buys apples or carrots.
what is the probability of a customer buying carrots?
1.4 percent 11.4 percent 5.0 percent 10.0 percent

Explanation:

Step1: Recall the formula for \(P(A\cup B)\)

The formula for the probability of the union of two events \(A\) and \(B\) is \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\). Let \(A\) be the event that a customer buys apples and \(B\) be the event that a customer buys carrots. We know that \(P(A) = 0.12\), \(P(A\cap B)=0.05\), and \(P(A\cup B)=0.17\).

Step2: Solve for \(P(B)\)

Substitute the known values into the formula \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\).

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Answer:

\(10.0\) percent