Discussion Forum

A bag contains 4 red and 6 black balls, a ball is drawn at random from the bag. Its colour is observed and this ball along with two additional balls of the same colour are returned to the bag. If now a ball is drawn at random from the bag, then the probability that this drawn ball is red, is

Answer:

Explanation:

Key Idea Use the theorem of total probability

Let E₁ = Event that first ball drawn is red

E₂ = Event that first ball drawn is black

  A= Event that second ball drawn is red

 P( E₁)= $\frac{4}{10}$, $P[\frac{A}{E_{1}}]=\frac{6}{12}$

$\Rightarrow$    $P(E_{2})=\frac{6}{10}, P(\frac{A}{E_{2}})=\frac{4}{12}$

By law of total probability

  $P(A_{})=P( E_{1})\times P(\frac{A}{E_{1}})+P(E_{2})\times P(\frac{A}{E_{2}})$

$=\frac{4}{10}\times \frac{6}{12}+\frac{6}{10}\times\frac{4}{12}$

$=\frac{24+24}{120}=\frac{48}{120}=\frac{2}{5}$