Question

Bag $B_1$ contains $4$ white and $2$ black balls. Bag $B_2$ cantains $3$ white and $4$ black balls. A bag is drawn at random and a ball is chosen at random from it. What is the probability that the ball drawn is white?

Answer 1

Let E denote the event of drawing while ball

$\Rightarrow P\left(E\right)=P\left(B_1\right)P\left(E/B_1\right)+P\left(B_2\right)P\left(E/B_2\right)$

$=\frac{1}{2}\times \frac{4}{6}+\frac{1}{2}\times \frac{3}{7}=\frac{1}{2}(\frac{2}{3}+\frac{3}{7})=\frac{1}{2}\left(\frac{14+9}{21}\right)=\frac{23}{42}$.