Question

By some miracle, a Smudgy Press book is found to have 90% of its pages free of typographic errors. Assuming that the distribution of the typographical errors per page is Poisson, what is the probability that a randomly selected page contains exactly one error

Answer 1

Answer:

The value is  $P(X = 1 ) = 0.0948$

Step-by-step explanation:

From the question we are told that

  The  the probability that the Smudgy Press book pages have zero  errors   $p = 0.90$

Gnerally the probability distribution for Poisson distribution is  

        $P(X = x) = \frac{\lambda ^x * e^{-\lambda}}{x!}$

Gnerally the probability that the Smudgy Press book pages have zero  errors is mathematically represented as

       $P(X = 0) = \frac{\lambda ^0 * e^{-\lambda}}{0!} =p= 0.90$

=>    $e^{-\lambda} =p= 0.90$

taking natural  log of both sides

       $ln (e^{-\lambda}) = ln(0.90)$

=>     $-\lambda = -0.1054$

=>   $\lambda = 0.1054$

Generally the probability that a randomly selected page contains exactly one error is mathematically represented as

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

=>       $P(X = 1 ) = \frac{0.1054 ^1 * e^{-0.1054 }}{1!}$

=>       $P(X = 1 ) = 0.0948$