In a county, 46% of the adults are males. One adult is randomly selected for a s
ID: 3132876 • Letter: I
Question
In a county, 46% of the adults are males. One adult is randomly selected for a survey involving credit card usage. Find the prior probability that the selected person is a female.It is later learned that the selected survey subject was smoking a cigar. Also, 8.3% of males smoke cigars, whereas 2.5% of females smoke cigars. Use this additional information to find the probability that the selected subject is female. P(Female) = (Type an integer or a decimal.) P(Female|Cigar) = (Round to three decimal places as needed.)Explanation / Answer
a.The probability that a randomly selected person is female is: 1-0.46=0.54
b.Using Bayes theorem find:
P(female given cigar)
=P(cigar given female)*P(female)/[ P(cigar given female)*P(female)+ P(cigar given male)*P(male)]
=0.025*0.54/(0.025*0.54+0.083*0.46)
=0.261