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?

There are 5 red and 5 black balls in the urn.

Let’s say the ball drawn in the first attempt is red.

(probability of drawing a red ball)

The urn now holds 7 red and 5 black balls with the addition of two balls of the same colour (red).

(probability of drawing a red ball)

Let’s say the ball sketched in the first try is black in colour.

(probability of drawing a black ball)

The urn now includes 5 red and 7 black balls, as well as two balls of the same colour (black).

(probability of drawing a red ball)

As a result, the probability of drawing the second red ball is: