#### Question

An urn contains 5 red and 5 black balls. A ball is drawn at random, its colour is noted and is returned to the urn. Moreover, 2 additional balls of the colour drawn are put in the urn and then a ball is drawn at random. What is the probability that the second ball is red?

#### Solution

The urn contains 5 red and 5 black balls.

Let a red ball be drawn in the first attempt.

∴P (drawing a red ball) `5/10 = 1/2`

If two red balls are added to the urn, then the urn contains 7 red and 5 black balls.

P (drawing a red ball) =`7/12`

Let a black ball be drawn in the first attempt.

∴ P (drawing a black ball in the first attempt) `5/10 = 1/2`

If two black balls are added to the urn, then the urn contains 5 red and 7 black balls.

P (drawing a red ball) = `5/12`

Therefore, probability of drawing second ball as red is `