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 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. What is the probability that two black balls are chosen?

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 black balls are choosen

Then the favourable events are B₁B₂, B₂B₁

i.e. 2

∴ Required probability = `2/12 = 1/6`