Typographic errors in a text are either nonword errors (as when “the” is typed a

Question

Typographic errors in a text are either nonword errors (as when “the” is typed as “teh”) or word errors that result in a real but incorrect word. Spell-checking software will catch nonword errors but not word errors. Human proofreaders catch 70% of word errors. You ask a fellow student to proofread an essay in which you have deliberately made 10 word errors. Missing 3 or more out of 10 errors seems a poor performance. What is the probability that a proofreader who catches 70% of word errors misses exactly 3 out of 10?

Explanation / Answer

P(catching any given error) = 70% = 0.7 P(missing any given error) = 30% = 0.3 P(missing exactly 3 and catching exactly 7 in a set of 10 given errors) = 0.3³ x 0.77 = 0.00222 ... = 0.22%

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