# 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.Write the sample space showing all possible outcomes.

$\begin{array}{1 1}(A)\;\{B_1B_2,W_1W_2\}\\(B)\;\{B_1B_2,W_1W_2,B_1W_1\}\\(C)\;\{B_1W_1,W_1B_2\}\\(D)\;\{B_1B_2,B_1W,B_2B_1,B_2B_1,B_2W,WB_1,WB_2,BW_1,BW_2,W_1B_1,W_1W_2,W_2B,W_2W_1\}\end{array}$

Given :
Urn $U_1:B_1,B_2,W$
Urn $U_2:B,W_1,W_2$
$\therefore$ The sample space is $S=\{B_1B_2,B_1W,B_2B_1,B_2B_1,B_2W,WB_1,WB_2,BW_1,BW_2,W_1B_1,W_1W_2,W_2B,W_2W_1\}$
Hence (D) is the correct answer.