Mr. Dupont is a professional wine taster. When given a French wine, he will identify it with probability ( 0.9 ) correctly as French, and will mistake it for a Californian wine with probability ( 0.1 ). When given a Californian wine, he will identify it with probability ( 0.8 ) correctly as Californian, and will mistake it for a
( mathrm{P} ) French wine with probability ( 0.2 ). Suppose that Mr. Dupont is given ten unlabelled glasses of wine, three with French and seven with Californian wines. He randomly picks a glass, tries the wine, and solemnly says : “French”. The probability that the wine he tasted was Californian, is nearly equal to
(A) ( 0.14 )
(B) ( 0.24 )
(C) ( 0.34 )
(D) ( 0.44 )
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