If there are 20 typographical errors randomly distributed in a 250-page document, the probability that a
given page contains exactly two errors is $0.3 \%$

Question

Quizplus · Accepted Answer

The probability of a page containing exactly two errors is given by the binomial distribution:$$P(X = k) = \binom{n}{k}p^k(1-p)^{n-k}$$where n is the number of trials, k is the number of successes, p is the probability of success, and (1-p) is the probability of failure.In this case, n = 20, k = 2, p = 0.003, and (1-p) = 0.997. Plugging these values into the formula, we get:$$P(X = 2) = \binom{20}{2}(0.003)^2(0.997)^{18} = 0.003$$Therefore, the probability of a page containing exactly two errors is 0.3%, which is the same as the given probability.

If There Are 20 Typographical Errors Randomly Distributed in a 250-Page