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There are three urns containing

   

white and

   

black balls,

   

white and

   

black balls, and

   

white and

   

black balls, respectively. There is an equal probability of each urn being chosen. A ball is drawn at random from the chosen urn and it is found to be white. Find the probability that the ball drawn was from the second urn.
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Given, we have

   

urns:

Urn

   

=

   

white and

   

black balls

Urn

   

=

   

white and 2 black balls

Urn

   

=

   

white and

   

black balls

Now, the probabilities of choosing either of the urns are

   

Let H be the event of drawing white ball from the chosen urn.

So,

   

and

   

By using Baye’s Theorem, we have

Therefore, the required probability is

   

.