Question

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 returned 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?

Answer 1

Zero

Explanation:

The probability of the ball being red after first selection is = (r) ÷ (r+b)

The probability of the ball being blue after first selection is = (b) ÷ (r+b)

If the ball selected is red, the total number of balls after its returned together with m number of red balls is = r+b+m

The probability of the selection doesn't depend on the second selection, hence condition probability is zero.

However the probability of the second selection depends on the first selection.