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

Independent marking with probability $5/6$ is Poisson thinning and gives a Poisson process of chip-buying arrivals, of rate $12(5/6)=10$ per hour. Its first arrival time therefore satisfiesFor example, its survival probability is $\mathbb{E}[(1/6{)}^{N(t)}]=\exp (12t(1/6-1))=e^{-10t}$, which also derives the thinning conclusion directly.