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 re(2): Solution + Spoiler (Ups...) by Jer)

Yeah, sorry about that.

After reading your post I though of another way to solve this without using graphs or trapezoids;

If the boy arrives between 12:20 and 12:40, there is obviously a 4/6 chance of them meeting. For the other time intervals the chance varies linearly from the extreme 2/6 at 12:00 (1:00) and 4/6, when arriving at 12:20 (12:40). The average of these two last probablities gives the average chance of them meeting between 12:00 and 12:20 or 1:40 and 1:00. The average of 2/6 and 4/6 is 3/6.

Thus whe have 3 regions of equal lenght (12:00 to 12:20, 12:20 to 12:40, and 12:40 to 1:00) that have a meeting probability of 3/6, 4/6, and 3/6, respectively. The average of these regions is the answer; 5/9.

In short, p = (4/6+2*(4/6+2/6)/2)/3 = 5/9.

Posted by ajosin on 2005-06-07 19:20:25