Q. 215.0( 3 Votes )

A bag contains 1 white and 6 red balls, and a second bag contains 4 white and 3 red balls. One of the bags is picked up at random and a ball is randomly drawn from it, and is found to be white in colour. Find the probability that the drawn ball was from the first bag.

Answer :

Given:


Bag I has 1 white and 6 red balls


Bag II has 4 white and 3 red balls


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


U1 = choosing Bag I


U2 = choosing Bag II


A = choosing white ball from urn


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




The Probability of choosing ball from each Bag differs from Bag to Bag and the probabilities are as follows:


P(A|U1) = P(Choosing white ball from Bag I)





P(A|U2) = P(Choosing white ball from Bag II)





Now we find


P(U1|A) = P(The chosen ball is from Bag I)


Using Baye’s theorem:







The required probabilities are .


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