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?

The probability of a customer buying carrots is 0.10.

Step-by-step explanation:

Here, given:

P (Customer buying apples) = 12%

⇒ P (A) = 12 / 100 = 0.12

P (Customer Buying apples AND Carrots) = 5%

⇒ P (A ∩ C) = 5 / 100 = 0.05

P (Customer buying apples OR carrots) = 17%

⇒ P (A∪ C) = 17/100 = 0.17

Now, we know that:

P (X ∪ Y) = P (X) + P (Y) - P (X ∩ Y)

Now, here substituting the values, we get:

P (A∪ C) = P (A) + P (C) - P (A ∩ C)

⇒ 0. 17 = 0.12 + P (C) - 0.05

or, 0.17 - 0.07 = P (C)

or, P (C) = 0.10

or, P (Customer Buying Carrots) = 0.10

Hence, the probability of a customer buying carrots is 0.10.