Consider randomly selecting a single individual and having that person test drive 3 different vehicles. define events a1, a2, and a3 by a1 5 likes vehicle [1 a2 5 likes vehicle [2 a3 5 likes vehicle [3 suppose that p(a1) 5 .55, p(a2) 5 .65, p(a3) 5 .70, p(a1 ø a2) 5 .80, p(a2 ù a3) 5 .40, and p(a1 ø a2 ø a3) 5 .88.

a. what is the probability that the individual likes both vehicle #1 and vehicle #2?

b. determine and interpret p(a2ua3).

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?