A sporting good company operates retail stores in the NY and Atlanta area. Custo

Question

A sporting good company operates retail stores in the NY and Atlanta area. Customers were asked to rate their shopping experiences, the results of which are summarized in the following table

Consider the following information

*67% of the customers who rated their store Poor came from the Philadelphia area

*36% of the customers who rated their store Average came from Philadelphia area

*30% f the customers who rated their store Good came from Philadelphia area

Use Bayes' Theorem to determine the probability that a customer who shopped in the Philadelphia are rated his or her experience as good.

Experience Percentage Poor 15 Average 45 Good 40

Explanation / Answer

Bayes' theorem. Let A1, A2, ... , An be a set of mutually exclusive events that together form the sample space S. Let B be any event from the same sample space, such that P(B) > 0. Then,

Note: Invoking the fact that P( Ak B ) = P( Ak )P( B | Ak ), Baye's theorem can also be expressed as

P( Ak | B ) =

SO 67% = 10

36%=16

30%=12

PROB =12/38

P( Ak ) P( B | Ak )/[P( A1 ) P( B | A1 ) + P( A2 ) P( B | A2 ) + . . . + P( An ) P( B | An )]

P( Ak | B ) = P( Ak B )/[P( A1 B ) + P( A2 B ) + . . . + P( An B )]

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