Q. 355.0( 3 Votes )

A is known to speak truth 3 times out of 5 times. He throws a die and reports that it is one. Find the probability that it is actually one.

Answer :

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


U1 = Getting 1 on throwing a die


U2 = Getting other than 1 on throwing a die


A = Reporting 1 after throwing the die


From the problem,




P(A|U1) = P(Reporting 1 on actually getting 1 on throwing a die)


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



P(A|U2) = P(Reporting 1 but not getting 1 on throwing a die)


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



Now we find


P(U1|A) = P(the die actually shows 1 given that man reports 1)


Using Baye’s theorem:






The required probability is .


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