There are two bags. Bag-1 contains 4 white and 6 black balls and Bag-2 contains 5 white and 5 black balls. A die is rolled, if it shows a number divisible by 3, a ball is drawn from Bag-1, else a ball is drawn from Bag-2. If the ball drawn is not black in colour, the probability that it was not drawn from Bag-2 is:

$\frac{2}{7}$

The correct answer is Option (3) → $\frac{2}{7}$

Probability of selecting

bag I = $P(I)=\frac{2}{6}=\frac{1}{3}$

bag II = $P(II)=\frac{2}{3}$

W → white ball selected

B → black ball selected

$P(W|I)=\frac{4}{10}$, $P(B|I)=\frac{6}{10}$

$P(W|II)=\frac{5}{10}$, $P(B|II)=\frac{5}{10}$

So P(Not black ball was drawn not from bag 2)

$=P(I|W)=\frac{P(I)P(W|I)}{P(I)P(W|I)+P(II)P(W|II)}$

$=\frac{1/3×4/10}{1/3×4/10+2/3×5/10}$

$=\frac{4}{4+10}=\frac{2}{7}$