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?

Given: An urn contains 5 red and 5 black balls.

Let in first attempt the ball drawn is of red colour.

⇒ P (probability of drawing a red ball)

Now the two balls of same colour (red) are added to the urn then the urn contains 7 red and 5 black balls.

⇒ P (probability of drawing a red ball)

Now Let in first attempt the ball drawn is of black colour.

⇒ P (probability of drawing a black ball)

Now the two balls of same colour (black) are added to the urn then the urn contains 5 red and 7 black balls.

⇒ P (probability of drawing a red ball)

Therefore, the probability of drawing the second ball as of red colour is:

5