Question

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 choosen at random. Next a ball is randomly chosen from the urn. Then a second ball is choosen at random from the same urn without replacing the first ball. What is the probability that two balls of opposite colour are choosen?

Answer 1

Given that one of the two urns is choosen

Then a ball is randomly choosen from the urn

Then a second ball is choosen at random from the same urn without replacing the first ball

If two balls of opposite colours are choosen then,

The required probability = `8/12 = 2/3`