Question

9.84. Suppose an urn has b blue balls and r red balls. An experiment consists of picking a ball at random from the urn, note its color and then put it back into the urn and add one more ball of the same color to the urn. Suppose we repeat this experiment twice. What is the probability that we get a blue ball in the second attempt?

Answer 1

Probabilty Tree diagram :

P(blue first) = b / (r+b)

Now if the first ball is blue, then 1 blue ball is added, hence the blue balls= b+1 and total balls = r+b+1

P(blue) = b+1/ (r+b+1)

P getting blue ball in first and second attempt :

P(first red) = r/ (r+b)

Now if the first ball is red, then 1 red ball is added, hence the blue balls= b and total balls = r+b+1

P(blue) = b/ (r+b+1)

P getting red in first attempt and blue ball in second attempt :

Hence, Probabilty of getting blue ball in second attempt :