Consider randomly selecting a single individual and having that person test drive 3 different vehicles. Define events A1, A2, and A3 by
A 1 =likes vehicle #1
A 2 =likes vehicle #2
A 3 =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 interpretP(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?
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