Question

Andrew and Bill are scheduled to meet at Starbucks at a set time, but they are often late for appointments. Each will arrive at Starbucks with a delay between 0 and 1 hour, with all pairs of delays being equally likely. Moreover, both Andrew and Bill shun the conveniences of the modern world, and thus they do not have cell phones to contact each other. The first person to arrive will wait for 20 minutes (1/3 of an hour) but will get impatient and leave in disgust if the other has not yet arrived by then. What is the probability that they will meet? Show/explain how you arrived at your answer.You can derive the answer any way you want. You can even draw a picture and argue convincingly from that, as long as you are precise in your statements.

Answer 1

hour into xi is the where be So there are then there X 18+ one are Ixt one will wait 20 or x20 min . ist Let, divide the time of o to I subparts. Xo, ki, ... nog event of i-minute late. Arrival of Andrew & Bill can total (61X61) possibility If the arrives at 21 possibility to (46, 4,,...,0) that they will meet [ Since the min so the and one has to come in No, x,,. one arrives at Similarly if the there are possibility (*1, R2 , X21). Then for R2, X3, 21 possibility for to so that they meet. If meet. If ist one arrives then there are 2o possibilities for and one (241, 242, . . . ,%). For x42 there are 18, & so P Total possibility of their arrival so 408 41x 21+ 20+ 19+ Probability 41x21 + 10x 21 = (21+51) 21 there cure 40 each at nal on for Xa3 there are 17, + they meet 5121 GIGI