Past exam of the options I course of the University of Oxford / 2013 / M / 1 / b / Solution

The first arrival time $T_1$, measured in hours after opening, has exponential distribution of rate twelve. ThereforeEquivalently, there must be no arrivals in the first quarter hour and at least one in the next; independent increments give $e^{-3}(1-e^{-3})$.