Alice Bob and Carl arrange to meet for lunch on a certain da

Alice, Bob, and Carl arrange to meet for lunch on a certain day. They arrive independently at uniformly distributed times between 1 pm and 1:30 pm on that day. What is the probability that Carl arrives first? For the rest of this problem. assume that Carl arrives first at 1:10 pm, and condition on this fact.

Solution

As each one arriving is independent, and each person is equally likely to come first,

Prob Carl arrives first = 1/3