Q. 43.7( 3 Votes )

The contents of t

Answer :

Given:


Urn I has 7 white and 3 black balls


Urn II has 4 white and 6 black balls


Urn III has 2 white and 8 black balls


Let us assume U1, U2, U3 and A be the events as follows:


U1 = choosing Urn I


U2 = choosing Urn II


U3 = choosing Urn III


A = choosing 1 white and 1 red ball from urn


From the problem,





The Probability of choosing balls from each Urn differs from Urn to Urn and the probabilities are as follows:


P(A|U1) = P(Choosing required balls from Urn 1)






P(A|U2) = P(Choosing required balls from Urn 2)






P(A|U3) = P(Choosing required balls from Urn 3)






Now we find


P(U3|A) = P(The chosen balls are from Urn3)


Using Baye’s theorem:







The required probabilities is .


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