Two people have to spend exactly 15 consecutive minutes in a bar on a given day, between 12:00 and 13:00. Assuming uniform arrival times, what is the probability they will meet?
I am mainly interested to see how people would model this formally. I came up with the answer 50% (wrong!) based on the assumptions that:
- independent uniform arrival
- they will meet iff they actually overlap by some $\epsilon > 0$
- we can measure time continuously
but my methods felt a little ad hoc to me, and I would like to learn to make it more formal.
Also I'm curious whether people think the problem is formulated unambiguously. I added the assumption of independent arrival myself for instance, because I think without such an assumption the problem is not well defined.