3. Suppose that A and B are events in a sample space S and that P(A), P(B) and P(A|B) are known. Show how to find a formula for P(A|B"). 4. A bag contains 25 red balls and 15 blue balls. Two are chosen at random one after the other, without replacement (ie, once you take the first one out, there are now 39 balls in the bag). (a) Use a tree diagram to help calculate the following probabilities: . the probability that both balls are red . the probability that the first ball is red and second is not . the probability that the first ball is red and the second is red . the probability that neither ball is red (b) What is the probability that the second ball is red? (c) What is the probability that at least one ball is red