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I'm new to statistics and having trouble with this question and was wondering if you guys could help me out. My question looks like this:

The number of calls an officer receives during a working day is a Poisson(5) random variable. The officer misses a call with probability 0.01 independently from call to call. Find the probability that the officer answers exactly 10 calls in a working day.

Thanks in advance!

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From general theory about the Poisson, suppose that the number of calls has Poisson distribution with parameter $\lambda$. Let $q$ be the probability that a call is answered. Then the number of answered calls also has Poisson distribution, with parameter $\lambda^\ast=q\lambda$.

In our case, $\lambda=5$ and $q=0.99$. So $\lambda^\ast=4.95$. If $Y$ has Poisson distribution with parameter $4.95$, it is easy to find $\Pr(Y=10)$.

Remark: A similar question came in less than $2$ weeks ago. I answered it, giving a full derivation of the fact that the resulting distribution is Poisson, with parameter the $\lambda$ of the incoming calls times the probability of not missing a call.

Added: Found the link!

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