Question

A bag contains 3 red and 2 black balls. One ball is drawn from it at random. Its colour is noted and then it is put back in the bag. A second draw is made and the same procedure is repeated. Find the probability of drawing (i) two red balls, (ii) two black balls, (iii) first red and second black ball.

Answer 1

_{$$\begin{gathered} \mathrm{Given}:\mathrm{Bag}\mathrm{contains}3\mathrm{red}\mathrm{and}2\mathrm{black}\mathrm{balls}. \\ \mathrm{Let}\mathrm{three}\mathrm{red}\mathrm{balls}\mathrm{be}\mathit{}{R}_1,\mathit{}{R}_{\mathit{2}}\mathit{}\mathrm{and}{R}_3\mathrm{and}2\mathrm{black}\mathrm{balls}\mathrm{be}{B}_1\mathrm{and}{B}_2\mathit{.} \\ \mathrm{Sample\; space:} \\ \{\left(R_1,R_2\right),\left(R_1,R_3\right),\left(R_1,B_1\right),\left(R_1,B_2\right),\left(R_1,B_3\right) \\ \left(R_2,R_3\right),\left(R_2,B_1\right),\left(R_2,B_2\right)\left(R_3,R_3\right) \\ \left(\mathrm{i}\right)P\left(drawingtworedballs\right)=\frac{9}{25} \\ \left(\mathrm{ii}\right)P\left(\mathrm{drawing\; two\; black}\right)=\frac{4}{25} \\ \left(\mathrm{iii}\right)P\left(\mathrm{first\; red\; and\; second\; black}\right)=\frac{6}{25} \end{gathered}$$}