A box P contains one white ball, three red balls and two black balls. Another box Q contains two white balls, three red balls and four black balls. If one ball is drawn at random from each one of the two boxes, then the probability that the balls drawn are of different colour is

Question

Aicharya · Accepted Answer

P (Two different colour balls from each one of the boxes) $\begin{aligned} & =\mathrm{W}_{\mathrm{P}} \mathrm{R}_{\mathrm{Q}}+\mathrm{R}_{\mathrm{P}} \mathrm{~W}_{\mathrm{Q}}+\mathrm{R}_{\mathrm{P}} \mathrm{~B}_{\mathrm{Q}}+\mathrm{B}_{\mathrm{P}} \mathrm{R}_{\mathrm{Q}}+\mathrm{B}_{\mathrm{P}} \mathrm{~W}_{\mathrm{Q}}+\mathrm{W}_{\mathrm{P}} \mathrm{~B}_{\mathrm{Q}} \\ & =\frac{1}{6} \times \frac{3}{5}+\frac{3}{6} \times \frac{2}{5}+\frac{3}{6} \times \frac{4}{9}+\frac{2}{6} \times \frac{3}{5}+\frac{2}{6} \times \frac{2}{5}+\frac{1}{6} \times \frac{4}{9} \\ & =\frac{9}{54}+\frac{18}{54}+\frac{8}{54}=\frac{35}{54} \end{aligned}$

A box P contains one white ball, three red balls and two black balls. Another box Q contains two white balls…

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