An urn has b black and r red balls. A ball is drawn and put back into the urn together with c balls of the same color. (So, now there are b+r+c balls in the urn.)
After that again a ball is drawn.

(a) Do you expect that the probability that the second ball is red, depends on c?

(b) Prove that this probability is the same as for the first ball: r/(b+r).

(c) Consider the probability that the first ball is red given that the second is red. Do you expect that this probability depends on c? Find it.