Q. 365.0( 2 Votes )

A speaks the truth 8 times out of 10 times. A die is tossed. He reports that it was 5. What is the probability that it was actually 5?

Answer :

Let us assume U1, U2 and A be the events as follows:


U1 = Getting 5 on throwing a die


U2 = Getting other than 5 on throwing a die


A = Reporting 5 after throwing the die


From the problem,




P(A|U1) = P(Reporting 5 on actually getting 5 on throwing a die)


P(A|U1) = P(Telling the truth)



P(A|U2) = P(Reporting 5 but not getting 5 on throwing a die)


P(A|U2) = P(Not telling the truth)



Now we find


P(U1|A) = P(the die actually shows 5 given that man reports 5)


Using Baye’s theorem:







The required probability is .


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