A city has 60 bicycle shops consisting of 35 brand A shops and 25 brand B shops.

Question

A city has 60 bicycle shops consisting of 35 brand A shops and 25 brand B shops. 33 of the 50 shops provide “good” services and the rest provide “not good” services. Let A denote the set of brand A shops, B denote the set of brand B shops, G denote the set of “good”service shops, NG denote the set of “not good” service shops. The classification of the 50 shops is summarized in the table below.

Compute P(A | G), P(G | A), P(B | G), P(G | B), P(NG | A), P(A | NG), P(NG | B), P(B | NG).

Explanation / Answer

P(A | G)=P(A and G)/P(G)=19/33

P(G | A)=P(A and G)/P(A)=19/35

P(B | G)=P(B and G)/P(G)=14/33

P(G | B)=P(B and G)/P(B)=14/25

P(NG | A)=P(NG and A)/P(A)=16/35

P(A | NG)=P(NG and A)/P(NG)=16/27

P(NG | B)=P(NG and B)/P(B)=11/25

P(B | NG)=P(NG and B)/P(NG)=11/27

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