A cupboard A has 4 red carpets and 4 blue carpets and a cupboard B has 3 red carpets and 5 blue carpets. A carpet is selected from a cupboard and the carpet is chosen from the selected cupboard such that each carpet in the cupboard is equally likely to be chosen. Cupboards A and B can be selected in ( frac{1}{5} ) and ( frac{3}{5} ) ways respectively. Given that a carpet selected in the above process is a blue carpet, find the probability that it came from the cupboard B.

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1.	A cupboard A has 4 red carpets and 4 blue carpets and a cupboard B has 3 red carpets and 5 blue carpets. A carpet is selected from a cupboard and the carpet is chosen from the selected cupboard such that each carpet in the cupboard is equally likely to be chosen. Cupboards A and B can be selected in ( frac{1}{5} ) and ( frac{3}{5} ) ways respectively. Given that a carpet selected in the above process is a blue carpet, find the probability that it came from the cupboard B.
A.	( frac{2}{5} )
B.	( frac{15}{19} )
C.	( frac{31}{73} )
D.	( frac{4}{9} )
Answer» C. ( frac{31}{73} )

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