In a city, 51% of the adults are males. (It doesn\'t take too much advanced math
ID: 3275209 • Letter: I
Question
In a city, 51% of the adults are males. (It doesn't take too much advanced mathematics to deduce that the other 49% are females.) Also, 9.5% of males smoke cigars, whereas 1.7% of females smoke cigars (based on data from the US-Substance Abuse and Mental Health Services Administration). One adult is randomly selected: a. Find the probability that the selected person is a male. b. It is later learned that the selected survey subject was smoking a cigar, use the above information to find the probability that the selected subject is a male.[Bayes rule]|Explanation / Answer
Answers to questins asked:
(a) 0.51
(b) 0.8539
EXPLANATION:
Smoke Not not smoke Total
Male 0.0485 0.4616 0.51
Female 0.0083 0.4817 0.49
Total 0.0568 0.9433 1.00
EXPLANATION: 9.5% of 0.51 = 0.0485.
1.7 % of 0.49 = 0.0083
(a) P(male) = 0.51
(b) Let
A = male
B = smoker
By Bayes rule:
P(A/B) = P(AB)/P(B) (1)
P(AB) = P(male & smoker) = 0.0485
P(B) = P(smoke) = 0.0568
Substituting in (1), we get:
P(A/B) = 0.0485/0.0568 = 0.8539