Alice, bob, and carl arrange to meet for lunch on a certain day. they arriveindependently at uniformly distributed times between 1 pm and 1: 30 pm on that day.(a) 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 onthis fact.(b) what is the probability that carl will be waiting alone for more than 10 minutes? (c) what is the probability that carl will have to wait more than 10 minutes until hisparty is complete? (d) what is the probability that the person who arrives second will have to wait morethan 5 minutes for the third person to show up?