Question

An urn initially contains 6 red and 8 green balls. Each time a ball is selected, its color is recorded, and it is replaced in the urn along with 2 other balls of the same color. Compute the probability that:

If the second ball selected is green, what is the probability that the first one was red?

Answer 1

Required probability = P(1st ball is red | 2nd ball is green)

= P(1st ball is red and 2nd ball is green) / P(2nd ball is green)

Now, P(1st ball is red and 2nd ball is green) =

{Since if the 1st ball is red, the 2 balls would be added, which would also be red}

Now, P(2nd ball is green) = P(1st ball is red and 2nd ball is green) + P(1st ball is green and 2nd ball is green)

=

{Since if the 1st ball is green, the 2 balls would be added, which would also be green}

Required probability =