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).