Question

One bag contains $5$ white and $3$ red balls, and a second bag contains $4$ white and $5$ red balls. From one of them, chosen at random, two balls are drawn: find the chance that they are of different colours.

Answer 1

Probability of choosing a bag out of two $=\frac{1}{2}$

So the chance of getting balls of different $=P\left(E\right)$ $=\frac{1}{2}(\frac{5\times 3}{{}^8{C}_2}+\frac{4\times 5}{{}^9{C}_2})$

$\Rightarrow P\left(E\right)=\frac{1}{2}(\frac{15}{28}+\frac{5}{9})\Rightarrow P\left(E\right)=\frac{275}{504}$