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\begin{document}
{\bf Question}
The customers of a certain newspaper seller arrive according to a
Poisson process at a rate of 1 customer per minute. What is the
probability that at least 5 minutes have elapsed since (i) the
last customer arrived, (ii) the next to last customer arrived?
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{\bf Answer}
$N$ = number of customers in 5 minutes $\sim P(5)$
\begin{description}
\item[(i)]
$P(N=0) = e^{-5} = 0.0067\ldots$
\item[(ii)]
$P(N=0) + P(N=1) = e^{-5} + 5e^{-5} = 0.0404\ldots$
\end{description}
(at least five minutes have elapsed since the next to last
customer arrived, if the last five minutes included either 0 or 1
customers)
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