Henry and Ann are waiting for a bus. They know from experience that if they wait for an hour, they will have a 90% chance of getting it. It is a chilly night, though, so Ann says, "Let's only stay out for 10 minutes."
Henry says, "If we only wait for 10 minutes, we will only have a 15% chance."
Ann replies, "Not true. We have a better chance than that." Is Ann right? If so, what is the probability that they getting on the bus?
If you assume the buses arrive regularly and Henry and Ann arrive at a random moment in the cycle (very strong assumptions, but we can do no better), the buses must come every $\frac {10}9$ hour. If they wait $10$ min $=\frac 16$ hour, they have $\dfrac {\frac 16}{\frac {10}9}=\frac 9{60}=0.15$ chance of getting a bus, so Henry is right. They might do well to study the bus schedule.
If the buses arrive randomly, the rate is to get one with $90\%$ chance in one hour is $\lambda=\ln 10$. The chance for one not to arrive in $\frac 16$ hour is $e^{\frac{-\lambda}6}\approx 0.68$ so Ann would be right-they would have $32\%$ chance of getting one.