Question

An urn contains 5 red and 7 green balls. A ball is drawn at random and its colour is noted. The ball is placed back into the urn along with another ball of the same colour. The probability of getting a red ball in the next draw is

• A. $\frac{65}{156}$
• B. $\frac{67}{156}$
• C. $\frac{79}{156}$
• D. $\frac{89}{156}$

Answer 1

The correct option is A $\frac{65}{156}$

Case I: If 1st draw is red ball the urn contains 6R & 7G balls for 2nd draw.

Case II: If 1st draw is G ball the urn contains 5R & 8G balls for 2nd draw.

So Req. Prob

$=\frac{5}{\underset{\left(1\mathrm{st}\mathrm{draw}\right)}{12}}\times \frac{6}{\underset{\left(2\mathrm{nd}\mathrm{draw}\right)}{13}}+\frac{7}{\underset{\left(1\mathrm{st}\mathrm{draw}\right)}{12}}\times \frac{5}{\underset{\left(2\mathrm{nd}\mathrm{draw}\right)}{13}}$

$=\frac{65}{156}$