Question

Bag -I contains 3 red and 4 black balls while another Bag -II contains 5 red and 6 black b alls . One ball is drawn at random from one of the bags and it is found to be red . Find the probability that it was drawn from Bag -II.

Answer 1

Let $E_1,E_2$ be the event of choosing bag 1 and bag 2 respectively.

$E$ be the event that the drawn ball is red.

Then,

$\begin{array}{c}P\left(E_1\right)=P\left(E_2\right)=\frac{1}{2}\\ P\left(E/E_1\right)=\frac{3}{7}\\ P\left(E/E_2\right)=\frac{5}{11}\\ ApplytheBayestheorem\\ P\left(E_2/E_1\right)=\frac{\frac{1}{2}\times \frac{5}{11}}{\frac{1}{2}\times \frac{3}{7}+\frac{1}{2}\times \frac{5}{11}}\\ =\frac{35}{68}\end{array}$