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. (d) What is the probability that the person who arrives second will have to wait more than 5 minutes for the third person to show up?

Solution

Required probability is probability for one person to come within 5 minutes.

Already first person has arrived

Hence required prob = prob (third person comes after 5 minutes)

= 5/30 = 1/6