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)
=[tex]\dfrac{\dfrac{49}{377}}{\dfrac{96}{377}}[/tex]
= 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
