A boy and a girl agree to meet in the park. Each will show up at a random time between 12:00 and 13:00, and wait for the other person 20 minutes, but not past 13:00.

What is the probability that they will actually meet?

(In reply to Solution + Spoiler by ajosin)

Similar reasoning, different answer.

I plotted the probability the girl would arrive at a good time as a function of the boy's arrival time.

The graph is three straight lines from 12:00,1/3 to 12:20,2/3 to 12:40,2/3 to 1:00,1/3

The are under this curve is the probability.  The two trapeziods each have area 1/6 (1/3 * 1/2) and the rectangle 2/9 (1/3*2/3)for a total of

1/6 + 2/9 + 1/6 = 5/9

I can't figure out who is right.

Posted by Jer on 2005-06-07 19:01:20