Question

Suppose that a book of 600 pages contains 40 print mistakes. Assume that these errors are randomly distributed throughout the book and the number of errors per page follows a Poisson distribution. The probability that all the 10 pages selected at random have no print mistakes is:

• A. \( \frac{1}{3}e^{-1} \)
• B. \( 2e^{-1/3} \)
• C. \( e^{-2/3} \)
• D. \( \frac{3}{5}e^2 \)

Hint:

Poisson Distribution Zero Event}
For \( X = 0 \), use \( P(X=0) = e^{-\lambda} \)
Multiply exponent when independent trials involved
Compute \( \lambda \) as average number of events per unit

Answer 1

The Correct Option is C

Average errors per page = \( \lambda = \frac{40}{600} = \frac{1}{15} \) Probability of 0 mistakes on a page = \( P(X = 0) = e^{-\lambda} = e^{-1/15} \) For 10 independent pages: \[ P = \left( e^{-1/15} \right)^{10} = e^{-10/15} = e^{-2/3} \]