#### Question

the billing department of a major credit card company attempts to control errors on customers billa. Suppose that occur according to a poisson distribution with a parameter. what is the probability that a customers bill selected at random will contain one error?

#### Solution

Verified#### Step 1

1 of 2Formula $\textbf{Poisson probability}$:

$P(X=k)=\dfrac{\lambda^k e^{-\lambda}}{k!}$

The errors occur according a Poisson distribution with some parameter $\lambda$.

The probability that a customers bill selected at random will contain one error is then the formula of Poisson probability evaluated at $k=1$.

$P(X=1)=\dfrac{\lambda^1 e^{-\lambda}}{1!}=\dfrac{\lambda e^{-\lambda}}{1}=\lambda e^{-\lambda}$

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