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In a book of 250 pages, there are 200 typographical errors. Assuming that the number of errors per page follow the Poisson law, then the probability that a random sample of 5 pages will contain no typographical error is
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Verified Answer
The correct answer is:
$e^{-4}$
According to the given information
$$
\begin{aligned}
& \quad \lambda=\frac{200}{250}=\frac{4}{5} \\
& \because \quad P(X=x)=\frac{e^{-\lambda}\left(\lambda^X\right)}{x !} \Rightarrow P(X=0)=e^{-\frac{4}{5}} \\
& \therefore \text { Required probability }=(P(X=0))^5=\left(e^{-4 / 5}\right)^5=e^{-4}
\end{aligned}
$$
Hence, option (a) is correct.
$$
\begin{aligned}
& \quad \lambda=\frac{200}{250}=\frac{4}{5} \\
& \because \quad P(X=x)=\frac{e^{-\lambda}\left(\lambda^X\right)}{x !} \Rightarrow P(X=0)=e^{-\frac{4}{5}} \\
& \therefore \text { Required probability }=(P(X=0))^5=\left(e^{-4 / 5}\right)^5=e^{-4}
\end{aligned}
$$
Hence, option (a) is correct.
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