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In Orange County, $$51\%$$ of the adults are males. (It doesn't take too much advanced
mathematics to deduce that the other $$49\%$$ are females.) One adult is randomly selected
for a survey involving credit card usage.

a. Find the prior probability that the selected person is a male.

b. It is later learned that the selected survey subject was smoking a cigar. Also, $$9.5\%$$
of males smoke cigars, whereas $$1.7\%$$ of females smoke cigars (based on data
from the Substance Abuse and Mental Health Services Administration). Use this
additional information to find the probability that the selected subject is a male.

males $$\rightarrow 51\%$$
females $$\rightarrow 49\%$$

(a) $$P(M)=51 \%$$

(b) $$P(M|S)=\frac{P(S | M) P(M)}{P(S)} $$

$$=\frac{0,095 \times 0.51}{P(S | M) P(M)+P(S | F) P(F)}=0.85$$

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