Some Background:
Tim goes to a popular restaurant that does not take any reservations for tables. It has been determined that the waiting times for a table are normally distributed with a mean of 18 minutes and standard deviation of 4 minutes
The Question:
Tim has been waiting for 15 minutes. Find the probability that he will be seated within the next five minutes.
My Question: Suppose $T$ is the random variable that represents the amount of time Tim spent at the restaurant, so $T \sim N(15, 4^2)$. The answer sheet says the above question can be answered by working out $P(T < 20 | T > 15)$. My question is why do you work it out that way instead of $P(15 < T <20 | T > 15)$
Actually this is very simple $P(T < 20 | T > 15) = P(15 < T < 20 | T > 15)$