Example 21 - A man is known to speak truth 3 out of 4 times - Bayes theoram

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  1. Chapter 13 Class 12 Probability
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Example 21 A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is a six. Find the probability that it is actually a six. Let S1 : man speaks the truth S2 : man lies E : six on the die We need to find the Probability that it is actually a six, if the man reports that it a six i.e. P(S1|E) P(S1|E) = 1 . ( | 1 ) 1 . ( | 1 )+ 2 . ( | 2 ) Putting value in formula, P(S1|E) = P(S1) . P(E|S1) P(S1) . P(E|S1) + P(S2) . P(E|S2) = 3 4 1 6 3 4 1 6 + 1 4 5 6 = 1 4 1 6 3 1 4 1 6 3 + 5 = 3 8 Therefore, required probability is

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