In a recent study, the following responses were obtained to the question, “do you favor recycling in your neighborhood? ”. given that a randomly selected response was "no opinion", what is the probability that it came from a female? round your result to 2 significant places after the decimal (for example, 0.86732 should be entered as 0.87).
yes no no opinion
male 92 48 47
female 78 63 49

Answer with Step-by-step explanation:

                       Yes         No         No Opinion

Male                  92         48           47

Female              78          63          49

Given that a randomly selected response was "No Opinion"

what is the probability that it came from a female?

It is a problem of conditional probability in which

A: response came from a female

B: Response is "No Opinion"

Total number of no opinions=49+47=96

Total outcomes=92+78+48+63+47+49=377

P(B)=96/377

A∩B: No opinion from a female

P(A∩B)=49/377

P(A|B)=P(A∩B)/P(B)   (by Baye's theorem)

         =

         = 49/96

        = 0.51

Hence, given that a randomly selected response was "No Opinion",the probability that it came from a female is:

0.51

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step-by-step explanation:

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