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September 23, 2014

September 23, 2014

Posted by **Tifini** on Tuesday, July 17, 2012 at 4:43pm.

how would i set this problem up and solve it??

- conditional probability -
**MathMate**, Tuesday, July 17, 2012 at 10:21pmDefine events

N=from NYC, hence N'=not from NYC

A=adolescents under 18, hence A'=over 18

Given:

P(A|N)=1.0 (prob. of under 18 given person is from NYC)

P(A|N')=0.6 (prob. of under 18 given given person is from elsewhere)

First calculate

probability of finding a person under 18,

P(A)=P(A|N)*P(N)+P(A|N')*P(N') [ Bayes thm]

=1.0*0.1+0.6*0.9

=0.64

Now we look for the probability that someone is from NYC given she's under 18

P(N|A)

=P(N∩A)/P(A) [cond. prob.]

=P(A∩N)/P(A) [commutativity]

=P(A|N)P(N)/P(A) [Bayes Thm]

=1.0*0.1/0.64

=0.156

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