Question

An urn contains 5 red and 7green 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
1. \(\frac{{65}}{{156}}\)
2. \(\frac{{67}}{{156}}\)
3. \(\frac{{79}}{{156}}\)
4. \(\frac{{89}}{{156}}\)

Answer 1

Correct Answer - Option 1 : \(\frac{{65}}{{156}}\)

Urn: 5 red balls and 7 green balls

Case (1):

If the ball drawn in the first draw is red, then the urn contains,

Urn: 6 red balls and 7 green balls

Probability to get red ball in the next draw

\({P_1} = \frac{5}{{12}} \times \frac{6}{{13}} = \frac{{30}}{{156}}\)

Case (1):

If the ball drawn in the first draw is green, then the urn contains

Urn: 5 red balls, 8 green balls

Probability to get red ball in the next draw

\({P_2} = \frac{7}{{12}} \times \frac{5}{{13}} = \frac{{35}}{{156}}\)

Total probability \(\left( P \right) = {P_1} + {P_2} = \frac{{65}}{{156}}\)