Q. 33.5( 2 Votes )

Three urns contai

Answer :

Given:


Urn I has 2 white and 3 black balls


Urn II has 3 white and 2 black balls


Urn III has 4 white, 1 black red 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 ball from an urn


We know that each urn is most likely to choose. So, probability of choosing a urn will be same for every Urn.





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


P(A|U1) = P(Choosing white ball from Urn 1)





P(A|U2) = P(Choosing white ball from Urn 2)





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





Now we find


P(U1|A) = P(The chosen balls are from Urn1)


Using Baye’s theorem:







The required probabilities is .


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