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?\no 1.4 percent\no 5.0 percent\no 10.0 percent\no 11.4 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?\no 1.4 percent\no 5.0 percent\no 10.0 percent\no 11.4 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 and $B$ is the event of buying carrots. Let $P(A) = 0.12$, $P(A\cap B)=0.05$ and $P(A\cup B)=0.17$.

Step2: Rearrange formula to solve for $P(B)$

$P(B)=P(A\cup B)+P(A\cap B)-P(A)$.

Step3: Substitute values

$P(B)=0.17 + 0.05-0.12$. $P(B)=0.1$.

Answer:

10.0 percent