# 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.

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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