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?

I think it is 280/360 = 7/9.

To see why, think about it from the boy's perspective. If he arrives at any minute between 12:20 and 12:40 there girl allways has a 40 min interval to arrive and succesfully meet the boy (for example, if the boy shows up at 12:25, the girl has the interval 12:05 - 12:45 to choose from to see the boy).

Outside the 12:20 to 12:40, for for every minute the boy is closer to  12:00 or to 13:00 the interval the grirl has to arrive decreases by one minute (for example, if the boy shows up at 12:50 the girl has the interval 12:30 to 1:00, to choose from to see the boy).

Adding up the total time interval the girl has for a succesfull meet form the boy's perspecive for each minute 12:00 to 1:00, I get  20+21+22+...+39+40+40+...+40+39+....+22+21+20 = 280 min (looks like the area of a trapezoid giving 280 min^2 if done continously instead of min by min). Doing the same thing for the total interval the girl has to chose from I get 60+60+60+....+60+60+60 =360 mine (looks like a square if done continously).

The ratio of the numbers is 280/360 = 7/9.

 

Posted by ajosin on 2005-06-07 18:43:06