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?
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:

Given: Urn contains 5 red and 5 black balls.

Let in first attempt the ball drawn is of red colour. (probability of drawing a red ball) After the two balls of the same colour (red) have been added to the urn, the urn will contain seven red balls and five black balls. (probability of drawing a red ball) Now let in first attempt the ball drawn is of black colour. (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. (probability of drawing a red ball) As a result, the likelihood of drawing the second ball as being of the colour red is as follows: 