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A man is known to speak the truth 4 out ...

A man is known to speak the truth 4 out of 5 times. He throws a die and reports that it is a four. Find the probability that it is actually a four.

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To solve the problem, we will use Bayes' theorem to find the probability that the die actually shows a four given that the man reports it as a four. ### Step-by-Step Solution: 1. **Define Events:** - Let \( E_1 \) be the event that the man speaks the truth. - Let \( E_2 \) be the event that the man does not speak the truth. - Let \( A \) be the event that the die shows a four. ...
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