Question

An urn contains $5$ red and $2$ green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red, is :

• A. $\frac{27}{49}$
• B. $\frac{21}{49}$
• C. $\frac{26}{49}$
• D. $\frac{32}{49}$

Answer 1

The correct option is D $\frac{32}{49}$

Let $E_1$ : Event of drawing green and adding red ball.
$E_2$ : Event of drawing red and adding green ball.
$G$ : Event of drawing a red ball in the second draw
$\therefore P\left(G\right)=P\left(E_1\right)\cdot P\left(G|E_1\right)+P\left(E_2\right)\cdot P\left(G|E_2\right)$
$\Rightarrow P\left(G\right)=\frac{2}{7}\times \frac{6}{7}+\frac{5}{7}\times \frac{4}{7}$
$\Rightarrow P\left(G\right)=\frac{32}{49}$