An urn contains r red balls and b blue balls. One ball is selected at random from this urn, its color is recorded and it is retu
rned to the urn along with m additional balls of the same color as chosen. Another single ball is randomly selected from the urn (now containing r b m balls) and it is observed that the ball is blue. What is the conditional probability that the first ball selected is red given that the 2nd ball selected is observed to be blue?