Q. 15.0( 1 Vote )

# The contents of the urns I,II,III are as follows:Urn I: 1 white, 2 black and 3 red ballsUrn II: 2 white, 1 black and 1 red ballsUrn III: 4 white, 5 black and 3 red balls.One urn is chosen at random and two balls are drawn. They happen to be white and red. What is the probability that they come from Urns I,II,III?

Given:

Urn I has 1 white, 2 black and 3 red balls

Urn II has 2 white, 1 black and 1 red balls

Urn III has 4 white, 5 black and 3 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 and 1 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 required balls from Urn 1)

P(A|U2) = P(Choosing required balls 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)

P(U2|A) = P(The chosen balls are from Urn2)

P(U3|A) = P(The chosen balls are from Urn3)

Using Baye’s theorem:

The required probabilities are .

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