I think I need a Venn Diagram for this but I am notsure. Non word errors make up

Question

I think I need a Venn Diagram for this but I am notsure. Non word errors make up to 25% of all errors. A humanproofreader will catch 90% of nonword errors and 70% of worderrors. What percent of errors will the proofreader catch? I don'tknow how to solve this. Of all the errors that the proof reader catches, what percentare non word errors? I think this is (.90)(.25) = 22.5% I think I need a Venn Diagram for this but I am notsure. Non word errors make up to 25% of all errors. A humanproofreader will catch 90% of nonword errors and 70% of worderrors. What percent of errors will the proofreader catch? I don'tknow how to solve this. Of all the errors that the proof reader catches, what percentare non word errors? I think this is (.90)(.25) = 22.5%

Explanation / Answer

Let E = event that the human proof reader will catch an error       A = event that the error thatoccured is a nonword error       B = event that the error thatoccured is a word error We are given;            Pr[A]= 0.25           Pr[E/A] = 0.9 and P[E/B] = 0.7        Probability that theproof reader catches an error = P[E]                             = P[A]*P[E/A] + P[B]*P[E/B]                              = 0.25*0.9 + 0.75*0.7                             = 0.225 + 0.525                             = 0. 75 Hence the proof reader will catch an errorroughly 75% of the time b] Of all the errors that the proof reader catches, what percentare non word errors? P[A/proof reader catches an error] = P[A and proof reader catches the error]/ P[proofreader catchesthe error] = P[A]*P[E/A] / 0.75 = 0.225/0.75 = 0.3

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