After some observations, the marketing research team of a chain of retail grocer
ID: 3041775 • Letter: A
Question
After some observations, the marketing research team of a chain of retail grocery stores found that 68% of all the customers go to the bakery department, 72% of all the customers go the dairy department and 58% of all the customers go to both the bakery and the dairy departments. Use B to denote the event that a randomly selected customer goes to the bakery department and D to denote the event that a randomly selected customer goes to the dairy department. Thus the information given above can be written as P (B)= 0.68, P (D)=0.72, and P(B D) =0.58.
(I already have the answers to these questions I just have no idea how to get the answers.)
33.What is the probability that a randomly selected customer goes to either the bakery department or the dairy department but not both?
36.If it is known that a randomly selected customer will go to the bakery department, what is the probability that this customer will also go to the dairy department?
38.If it is known that a randomly selected customer will go to the bakery department, what is the probability that this customer will not go to the dairy department?
39.If it is known that a randomly selected customer will go to the dairy department, what is the probability that this customer will also go to the bakery department?
40.If it is known that a randomly selected customer will go to the dairy department, what is the probability that this customer will not go to the bakery department?
Explanation / Answer
33) P(B or D ) = P(B) + P(D) - P(B and D)
= 0.68 + 0.72 - 0.58 = 0.82
36) P(D | B) = P( D and B)/ P(B)
= 0.58/0.68 = 0.85
38) P(not D | B) = P(not D and B)/P(B)
= (0.68 - 0.58)/0.68 = 0.15
39) P(B | D) = P(B and D)/P(D)
= 0.58/0.72 = 0.81
40) P(not B | D) = P(not B and D)/P(D)
= (0.72 - 0.58)/0.72 = 0.19