I recently read a math problem and, having not yet taken anything beyond calculus 1, was curious about how to solve it correctly.

Problem: Calculate the probability of two people meeting at the same location between 1 and 2 p.m. Assume both people show and person 1 will wait 15 minutes for person 2.

Doesn't this probability increase as the time frame shrinks? For example, Isn't there a much smaller chance the pair will meet if person 1 arrives at 1:00 vs arrives at 1:45 (the probability of meeting becomes 1).

Is this somewhat easily answered using basic statistics? Just curious if my thought process is accurate or way wrong.

  • $\begingroup$ Are we assuming a uniform distribution that person 2 shows up between 1pm and 2pm? similarly, are we assuming a uniform distribution that person 1 shows up between 1pm and 1:45pm? $\endgroup$ – Ian Coley Apr 12 '13 at 3:43
  • $\begingroup$ I believe so. The original problem didn't address that, but I based my logic on the assumption that if this occurred 'naturally' (in a sterile environment without distractions, barring the preferences for time etc.) it would be a normally a distributed probability. $\endgroup$ – injuryprone Apr 12 '13 at 3:57

enter image description here

That's an example for the case where person1 will wait 10 minutes = $\frac 1 6$ hour for person2. To find the needed probability you should just integrate the marginal density over the shaded area.

I am sure you can easily see any answers on your questions on this geometrical example.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.