Project ForgeConsider Guwahati (G) and Delhi (D) whose temperatures can be classified as high (H), medium (M) and low (L). The conditional probabilities P(HD|HG)=0.40, P(MD|HG)=0.48, P(LD|HG)=0.12, P(HD|MG)=0.10, P(MD|MG)=0.65, P(LD|MG)=0.25, P(HD|LG)=0.01, P(MD|LG)=0.50, P(LD|LG)=0.49 are given, along with P(HG)=0.2, P(MG)=0.5, P(LG)=0.3. The probability (correct to two decimal places) that Guwahati has high temperature given that Delhi has high temperature is ____.
Explanation
By the law of total probability: P(HD) = P(HD|HG)P(HG) + P(HD|MG)P(MG) + P(HD|LG)P(LG) = 0.40×0.2 + 0.10×0.5 + 0.01×0.3 = 0.08+0.05+0.003 = 0.133. By Bayes' theorem: P(HG|HD) = P(HD|HG)P(HG)/P(HD) = 0.08/0.133 ≈ 0.60.
Source: GATE CS 2018 (2018)
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