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?

Answer 1

Because an urn contains 5 red and 5 black balls.

(i) Suppose a red ball is drawn.

∴ Probability of drawing a red ball from a total of 10 balls = `5/10 = 1/2`

Now if two red balls are placed in the urn.

The urn contains 7 red and 5 black balls.

Probability of drawing a red ball = `7/12`

(ii) Let the black ball be drawn first.

Probability of drawing a black ball from a total of 10 balls = `5/10 = 1/2`

Two black balls are then placed in the urn.

Now the urn contains 5 red and 7 black balls.

The probability of getting a red ball = `5/12`

Probability of the second ball being red = `1/2 xx 7/12 + 1/2 xx 5/12`

= `7/24 + 5/24`

= `12/24`

= `1/2`