Probability — Class 12 Maths Solution

A ${\rm{box}} = \{ 5$ blue, $4{\rm{red}}\}$

Let ${E_1}$ is the event that first ball drawn is blue, ${E_2}$ is the event that first ball drawn is red and $E$ is the event that second ball drawn is blue.

$\therefore$ $P(E) = P\left( {{E_1}} \right) \cdot P\left( {E/{E_1}} \right) + P\left( {{E_2}} \right) \cdot P\left( {E/{E_2}} \right)$

$= \frac{5}{9} \cdot \frac{4}{8} + \frac{4}{9} \cdot \frac{5}{8} = \frac{{20}}{{72}} + \frac{{20}}{{72}} = \frac{{40}}{{72}} = \frac{5}{9}$