Two persons want to meet. They know the place where to meet. The time when one of them come to the place of meeting is equiprobable and lies in the $[0,T]$. Someone of them who comes first will wait $\tau$ minutes and go away. What is the probability of meeting?

Question

experimentx · Answer

I don't seem to understand this problem ... are they allowed to come at any time?

klimenkov · Answer

Yes. Any time from 0 to T. For example you want to meet your friend between 1 p.m and 2 p.m. This is the same.

klimenkov · Answer

$[0,T]$ is used to simplify.

experimentx · Answer

and how long will I wait?

klimenkov · Answer

For example, 15 minutes = 1/4 hour.

experimentx · Answer

I'm not good with probability ... but this question seems interesting ... since most of my friends always like about time and distance while waiting.

klimenkov · Answer

If you are interested I will give you a solution.

klimenkov · Answer

But firstly, I'd like you to solve another problem.

experimentx · Answer

hold on ... I'll wait.

klimenkov · Answer

If there are n balls in the very dark room and among them are m white and other n-m are black. What is the probability to take a white ball if you can see nothing and the probabilities for taking any of n balls are the same (equiprobable)?

experimentx · Answer

m/n??

klimenkov · Answer

Yes. Now lets try more complicated what is called a geometric probability. Someone want to hit the zone #1 by shooting from a gun. What is the probability to shot at zone #1 if the shooter always hit in the big circle? |dw:1350222646524:dw|