In a printing press of a publication house, there is a small chance \( \displaystyle\frac{1}{1000} \) for any typing error in 20 pages, then the number of pages containing no error in printing two volumes of an Encyclopedia containing total 10000 pages are :
[Given : e-0.02 = 0.9802]
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 9802
The chance of an error is small and the number of trials is large, so the number of errors X on a page follows a Poisson distribution. The given value \( e^{-0.02} \) fixes the mean number of errors per page:
\( \displaystyle m=np=20\times\frac{1}{1000}=0.02 \)
The probability that a page has no error:
\( \displaystyle P(X=0)=\frac{e^{-m}m^0}{0!} \)
\( \displaystyle =e^{-0.02}=0.9802 \)
The expected number of such pages out of 10000:
\( \displaystyle 10000\times 0.9802=9802 \)