Mr. Modi is a professional tea taster. When given a high grade tea, he will identify it with probability 0.9 correctly as high grade and will mistake it for a low grade tea with probability 0.1 . When given a low grade tea, he will identify it with probability 0.8 correctly as low grade tea and will mistake it for a high grade tea with probability 0.2 . Suppose that Mr. Modi is given ten unlabelled cups of tea, three with high grade and seven with low grade tea. He randomly picks a cup, tries the tea and solemnly says “high grade tea”. If the probability that the tea he tasted was low grade tea is express in form of a/b then (3a – b) equals. (Where a & b are co-prime natural numbers)
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Sol. P(identify high grade tea correctly) =
; P (identify low grade tea correctly) = 
P (Given high grade tea) =
; P (Given low grade tea) = 
P (Low grade tea / says high grade tea) =
= 
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