Q28 of 29 Page 1

A man is known to speak the truth 3 out of 4 times. He throws a dice and reports that it is a six. Find the probability that it is actually a six.

Formula Used: Given E1,E2,E3.....En are mutually exclusive and exhaustive events, we can find the conditional probability for any event A associated with Ei using the Bayes theorem as follows:



Let E be the event that the man reports that six occurs in the throwing of the die and let S1 be the event that six occurs and S2 be the event that six does not occur.




probability that the man reports that six occurs when 6 has actually occurred on the die.


probability that the man speaks the truth


probability that the man reports that six occurs when 6 has not actually occurred on the die.


probability that the man does not speak the truth


Hence, by Bayes theorem, we get,





Hence the required probability is


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