A magazine conducted a survey among its readers in a certain state. They reporte

Question

A magazine conducted a survey among its readers in a certain state. They reported the following results: Out of 1200 respondents, 312 are professionals, 470 are married, 524 are college graduates, 193 are professional college graduates, 178 are married college graduates, 136 are married professionals, and 35 are married professional college graduates. What is the probability that a randomly selected reader in that state is: (a) Either married, or a college graduate, or a professional? (b) Neither married, nor a college graduate, nor a professional?

Explanation / Answer

let professional are A married are B and college graduates are C.

therefore

a)

respondents   Either married, or a college graduate, or a professional =

hence probability=834/1200=0.695

b)

P(Neither married, nor a college graduate, nor a professional) =1-P(either one of them) =1-0.695 =0.305

N(T)= 1200 N(A)= 312 N(B)= 470 N(C)= 524 N(AnB)= 136 N(BnC)= 178 N(AnC)= 193 N(AUB)= 646 N(BUC)= 816 N(AUC)= 643 N(AnBnC) = 35

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