the manager of a grocery store reports that there is a 12 percent chance that a customer buys apples during…

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
Answer
Answer:
10.0 percent
Explanation:
Step1: Recall probability formula
Let (P(A)) be the probability of buying apples, (P(C)) be the probability of buying carrots, and (P(A\cap C)) be the probability of buying both. The formula for (P(A\cup C)) is (P(A\cup C)=P(A)+P(C)-P(A\cap C)).
Step2: Identify given values
We know that (P(A) = 0.12), (P(A\cap C)=0.05), and (P(A\cup C)=0.17).
Step3: Rearrange formula to solve for (P(C))
(P(C)=P(A\cup C)+P(A\cap C)-P(A)).
Step4: Substitute values
(P(C)=0.17 + 0.05-0.12).
Step5: Calculate result
(P(C)=0.10) or 10.0 percent.