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# Probability that A speaks truth is. A coin is tossed and reports that a head appears. What is the probability that actually there was head? Do you think that A needs to improve his acquired life values about truth?

Asked by Topperlearning User 1st March 2013, 9:03 AM

Let E be the event that the A reports that head appears in the throwing of the die and let S1 be the event that head appears and S2 be the event that head does not appear.

P(E | S1) = Probability that A reports that head appears when head has actually appeared on the coin = Probability that A speaks the truth =

P(E | S2) = Probability that A reports that head appears when head has not appeared on the coin = Probability that A does not speak the truth =

Thus, by Bayes theorem, we get

P(S1 | E) = Probability that the report of A that head has appeared is actually a head

Yes, as A speaks truth 5 times out of 9, i.e., only 55%, which is very much on lower side.

Answered by Expert 1st March 2013, 11:03 AM
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