Consider randomly selecting a single individual and having that person test drive 3 different vehicles.
Define events $A_1, A_2, A_3$ by:
- $A_1$ = likes vehicle #1
- $A_2$ = likes vehicle #2
- $A_3$ = likes vehicle #3
Suppose that $P(A_1) = .55 \,, P(A_2) = .65 \,, P(A_3) = .7 \,, P(A_1 \cup A_2) = .8 \,, P(A2 \cap A3) = .4, \,, P(A1 \cup A2 \cup A3) = .88$
(a) What is the probability that the individual likes both vehicle #1 and vehicle 2?
(b) Determine and interpret $P(A_2 \mid A_3)$
(c) Are $A_2$ and $A_3$ independent events? Answer in two different way.
(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?
I am stuck on the fourth part. What I have done so far : I am thinking $P(A_2 \mid A_1') + P(A_3 \mid A_1') + P(A_3 \cap A_2 \mid A_1')$