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?

Explanation

The urn contains 5 red and 5 black balls.
Let a red ball be drawn in the first attempt. Therefore,
P(drwing a red ball) `=5/10=1/2`
If two red ball are added to the urn, then the urn contains 7 red and 5 black balls. Thus.
P (drawing a red ball) `=7/12`
Let a black ball be drawn in the first attempt. Then
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 the second ball as red is
`1/2xx7/12+1/2xx5/12=1/2((1)/(12)+(5)/(12))=1/2xx1=1/2`