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.\nwhat is the probability of a customer buying carrots?\n1.4 percent\n5.0 percent\n10.0 percent\n11.4 percent

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.\nwhat is the probability of a customer buying carrots?\n1.4 percent\n5.0 percent\n10.0 percent\n11.4 percent

Answer

Explanation:

Step1: Recall probability formula

Use the formula $P(A\cup B)=P(A)+P(B)-P(A\cap B)$, where $A$ is the event of buying apples, $B$ is the event of buying carrots, $P(A\cup B)$ is the probability of buying apples or carrots, $P(A)$ is the probability of buying apples, and $P(A\cap B)$ is the probability of buying apples and carrots.

Step2: Identify given values

We know that $P(A) = 0.12$, $P(A\cap B)=0.05$, and $P(A\cup B)=0.17$.

Step3: Solve for $P(B)$

Substitute the values into the formula: $0.17 = 0.12+P(B)- 0.05$. First, simplify the right - hand side: $0.12 - 0.05+P(B)=0.07 + P(B)$. Then, solve for $P(B)$: $P(B)=0.17 - 0.07=0.10$.

Answer:

10.0 percent