Question

an armored car transports money between two locations and travels along one of the three routes: A1,B1,C1. On one day, the route is randomly selected according to the probabilities P(A1)=0.4, P(B1)=0.2, P(C1)=0.4. However, on the second day, the probabilities change so that the probability of the previously chosen route is 0.2 with the other two routes equally probable. Denote those second-day routes by A2, B2, C2. Find P(A2|A1).

Answer 1

We know the probabilities of selecting different routes on first day.

We need to find P(A2 | A1). This means that we need to find the probability of A2, when it is known that the route chosen on day 1 is A1. If a route is taken on first day , then the probability of taking the same route on the next day is 0.2. In the question also we need to find the probability of choosing route A on second day when it is given the on first day also, the chosen road was A. So the required probability will be 0.2.