Three boxes numberedas I. II, III contain 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 frorn it. lf the ball is red, then the probability that it is from box Il.

Let A₁, A₂, A₃ denote the events of selecting box I, box II, box III respectively and let E denote the event of drawing a red ball from the selected box. 

Now $P\left(A_1\right)=1/3,P\left(A_2\right)=1/3,P\left(A_3\right)=1/3$

$P\left(E\mid A_1\right)=3/6=1/2,P\left(E\mid A_2\right)=1/4,P\left(E\mid A_3\right)=3/12\Rightarrow 1/4$

By Baye's theorem, $P\left(A_2\mid E\right)=\frac{P\left(A_2\right)P\left(E\mid A_2\right)}{\Sigma P\left(A_j\right)P\left(E\mid A_i\right)}=\frac{(1/3)(1/4)}{(1/3)[1/2+1/4+1/4)}=\frac{1}{4}$