Question

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?

Answer 1

Answer:

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.