Question

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 1

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)

         =$\dfrac{\dfrac{49}{377}}{\dfrac{96}{377}}$

         = 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