Q. 185.0( 2 Votes )

Three urns A,B and C contain 6 red and 4 white; 2 red and 6 white; and 1 red and 5 white balls respectively. An urn is chosen at random and a ball is drawn. If the ball drawn is found to be red, find the probability that the ball was drawn from urn A.

Answer :


Urn A has 6 red and 4 white balls

Urn B has 2 red and 6 white balls

Urn C has 1 red and 5 white balls

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

U1 = choosing Urn A

U2 = choosing Urn B

U3 = choosing Urn C

A = choosing red ball from 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 red ball from Urn A)

P(A|U2) = P(Choosing red ball from Urn B)

P(A|U3) = P(Choosing red ball from Urn C)

Now we find

P(U1|A) = P(The red ball is from Urn A)

Using Baye’s theorem:

The required probability is .

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