An urn contains m white and n black balls. A ball is drawn at random and is put back into the urn along with k additional balls of the same colour as that of the ball drawn. A ball is again drawn at random. Show that the probability of drawing a white ball now does not depend on k.

Question

Philoid · Accepted Answer

Given that an urn contains m white and n black balls.

Let E₁ = first ball drawn of white colour

E₂= first ball drawn of black colour

And E₃= second ball drawn of white colour

∴

Also,

Using the probability theorem, we have:

∴P(E₃) = P(E₁). P () +P(E₂).

Hence, the probability of drawing a white ball does not depend on k.