Consider randomly selecting a single individual and having that person test drive 3 different vehicles. Define events

Question:

Consider randomly selecting a single individual and having that person test drive 3 different vehicles. Define events A1, A2, and A3 by
A1 = likes vehicle #1
A2 = likes vehicle #2
A3 = likes vehicle #3
Suppose that P(A1) = .55, P(A2) = .65, P(A3) = .70, P(A1 ⋃ A2) = .80, P(A2 ⋂ A3) = .40, and P(A1 ⋃ A2 ⋃ A3) = .88.
a. What is the probability that the individual likes both vehicle #1 and vehicle #2?
b. Determine and interpret P(A2 ⋂ A3).
c. Are A2 and A3 independent events? Answer in two different ways.
d. If you learn that the individual did not like vehicle #1, what now is the probability that he/she liked at least one of the other two vehicles?