Problem - Fuel Consumption and Cars Auto Parts Warehouse offers a wide variety of parts and accessories for cars. Consider the following events:

A = a randomly selected customer purchases a manual

B = a randomly selected customer purchases trim accessories

C = a randomly selected customer purchases a car-care product

Suppose the following probabilities are known.

P(A) = 0.44, P(B) = 0.52, P(C) = 0.39,

P(A∩B) = 0.19, P(A∩C) = 0.10, P(B∩C) = 0.23,

P(A∩B∩C) = 0.08

a. Carefully sketch a Venn diagram illustrating the relationship among these three events and label each region with the corresponding probability.

b. Find the probability of just event A occurring.

c. Find the probability of none of the events (A, B, or C) occurring.

d. Find P(A|C), P(B|A∩C), and P(A∩B∩C|A).