One urn contains two black balls (labelled B1 and B2) and one white ball. A second urn contains one black ball and two white balls (labelled W1 and W2). Suppose the following experiment is performed. One of the two urns is chosen at random. Next a ball is randomly chosen from the urn. Then a second ball is chosen at random from the same urn without replacing the first ball. Write the sample space showing aol possible outcomes. What is the probability that two black balls are chosen? What is the probability that two balls of opposite colour are chosen?

Explanation

It is given that one of the two urn is chosen, then a ball is randomly chosen from the urn, then a second ball is chosen at random from the same urn without replacing the first ball.
(i) `therefore"Sample space S"={B_(1)B_(2),B_(1)W,B_(2)B_(1),B_(2)W,WB_(1),WB_(2),BW_(1),BW_(2),W_(1)B,W_(1)W_(2),W_(2)B,W_(2),W_(1)}`
`therefore "total sample point=12"`
(ii) `"If two black ball are chosen."`
`"So, the favourable events are " B_(1)B_(2),B_(2)B_(1),i.e.,2`
`therefore"Required probability"=(2)/(12)=(1)/(6)`
(iii) `"If two balls of opposite colour are chosen."`
`"So the fourable events are "B_(1)W_(1),B_(2)W_(1),WB_(1),WB_(2)BW_(1),BW_(2),W_(1)B_(1),W_(2)Bi.e.,8.`
`therefore"Required probability"=(8)/(12)=(2)/(3)`