In a book of 250 pages,there are 200 typograp | vedclass

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Question

(A) Given that the total number of pages is $250$ and the total number of errors is $200$. The average number of errors per page,denoted by $\lambda$,

Vedclass · Accepted Answer

$e^{-4}$

Vedclass · Answer

(A) Given that the total number of pages is $250$ and the total number of errors is $200$. The average number of errors per page,denoted by $\lambda$,is calculated as: $\lambda = \frac{200}{250} = \frac{4}{5} = 0.8$. The Poisson probability distribution is given by $P(X=x) = \frac{e^{-\lambda} \lambda^x}{x!}$. The probability that a single page contains no error $(x=0)$ is: $P(X=0) = \frac{e^{-0.8} (0.8)^0}{0!} = e^{-0.8} = e^{-4/5}$. For a random sample of $5$ pages,the probability that none of them contain any error is: $P = (P(X=0))^5 = (e^{-4/5})^5 = e^{-4}$. Thus,the correct option is $A$.

$X$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$
$P(X=x)$	$0.15$	$0.23$	$0.12$	$0.10$	$0.20$	$0.08$	$0.07$	$0.05$

$X = x$	$0$	$1$	$2$	$3$	$4$
$P(X = x)$	$k$	$2k$	$4k$	$2k$	$k$

In a book of $250$ pages,there are $200$ typographical errors. Assuming that the number of errors per page follows the Poisson distribution,the probability that a random sample of $5$ pages will contain no typographical error is

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