Question

suppose that a book of 600 pages contains 40 printing mistakes. assume that these errors are randomly distributed throughout the book and x, the number of errors per page has a poisson distribution. what is the probability that 10 pages selected at random will be free of error ?

Answer 1

Given : A book of 600 pages contains 40 printing mistakes.

errors are randomly distributed throughout the book

 the number of errors per page has a Poisson distribution.  

To Find :  the probability that 10 pages selected at random will be free of error

Solution:

 600 pages contains 40 printing mistakes

=> 1 page contains =  40/600  = 4/60  mistakes

=> 10 pages contains = 10 * 4/60  = 4/6 mistakes  = 2/3  mistakes

Mean error is 10 pages  λ = 2/3  

P(x)  = λˣ  e^(-λ) / x!

10 pages selected at random will be free of error

=> x = 0  ( no error)

P (0) = (2/3)⁰  $e^{-\frac{2}{3 }$ / 0!

=  1/ $e^{\frac{2}{3 }$

≈ 0.51

the probability that 10 pages selected at random will be free of error  = 0.51

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