One urn contains two black balls (labelled $B_1,B_2$) and one white ball.A second urn contains one black ball and two white balls (labelled $W_1,W_2$).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? - Clay6.com, a Free resource for your JEE, AIPMT and Board Exam preparation

One urn contains two black balls (labelled $B_1,B_2$) and one white ball.A second urn contains one black ball and two white balls (labelled $W_1,W_2$).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?

$\begin{array}{1 1}(A)\;\large\frac{1}{6}\\(B)\;\large\frac{1}{4}\\(C)\;\large\frac{1}{5}\\(D)\;\text{None of these}\end{array} $