The three major options on a car model are an automatic transmission (A), a sunroof (B), and an upgraded stereo (C). The probabilities that a customer requests these options are as follows: P(A) = 0.70 P(B) = 0.80 P(C) = 0.75 P(A and B) = 0.65 P(A and C) = 0.55 P(B and C) = 0.60 P(A and B and C) = 0.53

Compute the probabilities of the following events.

a) Make a Venn diagram of the events A, B, and C. , mark the probabilities of every intersection involving these events.

Use this diagram for parts b) through d).

b) What is the probability that the next customer will select none of the three options? Show all your work.

c) What is the probability that the next customer will request only an automatic transmission and neither of the other two options? Show all your work.

d) If a customer requests a sunroof, what is the probability that he or she will request an upgraded stereo?

e) If a customer does not request a sunroof, what is the probability that he or she will request an upgraded stereo?