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A man is known to speak truth 3 out of ...

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.

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To solve the problem step by step, we will use Bayes' theorem to find the probability that the die actually shows a six given that the man reported it as a six. ### Step 1: Define the Events - Let \( S_1 \): the event that the man speaks the truth. - Let \( S_2 \): the event that the man lies. - Let \( E \): the event that the die shows a six. ### Step 2: Identify Known Probabilities ...
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