Question

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 5.0 percent 10.0 percent 11.4 percent

Explanation:

Step1: Use the formula for the probability of the union of two events

The formula for \(P(A\cup C)=P(A)+P(C)-P(A\cap C)\), where \(A\) represents the event of buying apples and \(C\) represents the event of buying carrots.
Let \(P(A) = 0.12\), \(P(A\cap C)=0.05\), and \(P(A\cup C)=0.17\).

Step2: Rearrange the formula to solve for \(P(C)\)

From \(P(A\cup C)=P(A)+P(C)-P(A\cap C)\), we can get \(P(C)=P(A\cup C)+P(A\cap C)-P(A)\).
Substitute the values: \(P(C)=0.17 + 0.05-0.12\).

Step3: Calculate the value of \(P(C)\)

\(P(C)=0.17+0.05 - 0.12=0.1\) or \(10\%\)

Answer:

10.0 percent