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.