2. The following information is about adults who live in the fictitious city of

Question

2. The following information is about adults who live in the fictitious city of Nalmer.

85% of the adults with a PhD have attended an out-of-town conference within the past year.

85% of the adults without a PhD have not attended an out-of-town conference within the past year.

10% of all adults have a PhD.

What is the probability that an adult resident of Nalmer who attended an out-of-town conference this past year has a PhD? Report your answer with a minimum of three digits after the decimal point

Explanation / Answer

P(Attended out of town conference | PhD) = 0.85

P(Attended out of town conference | not a PhD) = 1 - P(Not attended out of town conference | not a PhD)

= 1 - 0.85 = 0.15

P(PhD) = 0.10

P(Not a PhD) = 1 - 0.10 = 0.90

By theorem of total probability,

P(Attended out of town conference) = P(Attended out of town conference | PhD)*P(PhD) + P(Attended out of town conference | not a PhD)*P(Not a PhD)

= 0.85*0.10 + 0.15*0.90

= 0.22

By Bayes' theorem,

P(PhD | Attended out of town conference) = P(Attended out of town conference | PhD)*P(PhD) / P( P(Attended out of town conference)

= 0.85*0.10 / 0.22

= 0.386

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