MATH SOLVE

2 months ago

Q:
# 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 OpinionMale 92 48 47Female 78 63 49

Accepted Solution

A:

Answer with Step-by-step explanation: Yes No No Opinion
Male 92 48 47
Female 78 63 49Given 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 whichA: response came from a femaleB: Response is "No Opinion"Total number of no opinions=49+47=96Total outcomes=92+78+48+63+47+49=377P(B)=96/377A∩B: No opinion from a femaleP(A∩B)=49/377P(A|B)=P(A∩B)/P(B) (by Baye's theorem) =[tex]\dfrac{\dfrac{49}{377}}{\dfrac{96}{377}}[/tex] = 49/96 = 0.51Hence, given that a randomly selected response was "No Opinion",the probability that it came from a female is:0.51