**Solution:**

It is given that one urn contains two black balls and one white ball

and the second urn contains one black ball and two white balls.

Also given that if one of the two urns is chosen, then a ball is randomly chosen from the urn, then the second ball is chosen at random from the same urn without replacing the first ball.

**(a)** Sample Space

The total no. of sample space

**(b)** If the two black balls are chosen

The total outcomes

The favourable outcomes are

The total favourable outcomes

It is known that,