Question

There are 3 red and 2 white balls in one box and 4 red and 5 white in the second box. You select a box at random and from it pick a ball at random. If the ball is red, what is the probability that it came from the second box?

Short answer

The Probability is found to be $p(S/R)=\frac{20}{47}$and it can be shown with the picture given below.

Step-by-step solution

Given Information. 

It has been given that there are 3 red and 2 white balls in one box and 4 red and 5 white in the second box.

 Step 2: Definition of Probability.

Probability means the chances of any event to occur is called it probability.

Find the probability.

Find the Probability of the red ball.

$\begin{array}{c}{\text{p(R)=p}}_{\text{1}}{\text{R+p}}_{\text{2}}\text{R}\\ =0.5\times \frac{3}{5}+0.5\times \frac{4}{9}\\ =\frac{47}{90}\end{array}$n

If the ball is red the probability that it comes from the second box is derived below.

$\begin{array}{c}p(S/R)=\frac{p\left(SR\right)}{p\left(R\right)}\\ =\frac{0.5\times \frac{4}{9}}{47/90}\\ =\frac{20}{47}\end{array}$

Draw the diagram to show the situation. 

The situation is shown below.

The Probability is shown below.