An urn contains 6 red balls and 3 blue balls. One ball is selected at random and is replaces by a ball of the= other color. A Second ball is then chosen. What is the conditional probability that the first all selected is red, given that the second ball was red?

Question

venomblast · Answer

R_1 - First ball Red, R_2-second ball is red
P(R_1|R_2)=P(R_1 AND R_2)/P(R_2)

P(R_1 AND R_2) = 6/9 * 5/9 = 30/81=10/27
P(R_2) =  6/9 * 5/9 + 3/9 * 6/9 = 16/27

P(R_1|R_2)=(10/27)/(16/27) = 5/8.
I got it wrong. Why?