Question

Three boxes numbered I, II, III contains the balls as follows:

	White	Black	Red
I	$1$	$2$	$3$
II	$2$	$1$	$1$
III	$4$	$5$	$3$

One box is randomly selected and a ball is drawn from it. If the ball is red, then find the probability that it is from box II

Answer 1

Probability of a red ball being drawn from box I is $\frac{3}{1+2+3}=\frac{1}{2}$.

Probability of a red ball being drawn from box II is $\frac{1}{1+2+1}=\frac{1}{4}$.

Probability of a red ball being drawn from box III is $\frac{3}{4+5+3}=\frac{1}{4}$.

Now, given that we have the red ball, the probability that it has been drawn from box II becomes $\frac{\frac{1}{4}}{\frac{1}{2}+\frac{1}{4}+\frac{1}{4}}=\frac{1}{4}$.