= 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 satisfies
$$
\boxed{T_{\rm chips}\sim\operatorname{Exp}(10\text{ per hour}),\qquad\mathbb E T_{\rm chips}=\frac1{10}\text{ hour}=6\text{ minutes}.}
$$
For 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.
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