Q. 33.5( 2 Votes )

Three urns contains 2 white and 3 black balls; 3 white and 2 black balls; 4 white and 1 black balls respectively. One ball is drawn from an urn chosen at random and it was found to be white. Find the probability that it was drawn from the first urn.

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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