Question

There are 2 bags, one containing 4 red and 5 blue balls and the other containing 6 black and 2 white balls. One ball from each bag is taken out. What is the probability that the balls are i)red and black ii)blue and white iii)red and white iv)blue and black.

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right)\mathrm{Probability}\mathrm{of}\mathrm{red}\mathrm{and}\mathrm{black}=\frac{4}{9}\times \frac{6}{8}=\frac{1}{3} \\ \left(\mathrm{ii}\right)\mathrm{Probability}\mathrm{of}\mathrm{blue}\mathrm{and}\mathrm{white}=\frac{5}{9}\times \frac{2}{8}=\frac{5}{36} \\ \left(\mathrm{iii}\right)\mathrm{Probability}\mathrm{of}\mathrm{red}\mathrm{and}\mathrm{white}=\frac{4}{9}\times \frac{2}{8}=\frac{1}{9} \\ \left(\mathrm{iv}\right)\mathrm{Probability}\mathrm{of}\mathrm{blue}\mathrm{and}\mathrm{black}=\frac{5}{9}\times \frac{6}{8}=\frac{5}{12} \end{gathered}$$