Question

algebra i b-cr
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: Recall addition rule for probability

For events A (buys apples) and C (buys carrots), the addition rule is:
$$P(A \cup C) = P(A) + P(C) - P(A \cap C)$$

Step2: Rearrange to solve for $P(C)$

Isolate the unknown probability of buying carrots:
$$P(C) = P(A \cup C) - P(A) + P(A \cap C)$$

Step3: Substitute given values

Plug in $P(A)=0.12$, $P(A \cap C)=0.05$, $P(A \cup C)=0.17$:
$$P(C) = 0.17 - 0.12 + 0.05$$

Step4: Calculate the result

Compute the arithmetic:
$$P(C) = 0.10$$

Answer:

10.0 percent