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Answer to Question #447 in Statistics and Probability for Anna

Question #447
The book of 500 pages contains 50 misprints. Estimate the probability that a randomly selected page contains at least 3 misprints.
Expert's answer

The probability that a randomly selected page has a misprint is 50/500=1/10.
The probability that a randomly selected page has 2 misprints is (50/500)*(49/500) = 49/5000.
...
The probability that a randomly selected page has 50 misprints is (50/500)*(49/500)*...*(1/500) = 50!/((500)^50).
The probability that a randomly selected page has no misprints is 1 – 50/500 – 49/5000 – ... – 50!/((500)^50).

Considered event: there is not less than 3 misprints, i.e. any event other than 0, 1 or 2 misprints.
The probability of such an event is: P = 1 – (1–50/500–49/5000–...–50!/(500^50)) – 50/500 – 49/5000 = 50*49*48/500^3 + 50*49*48*47/500^4 + ... + 50!/500^50 ≈ 0,023

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