conditional probability

35. Let A be the event that all of a family's children are the same gender, and let B be the event that the family has at most 1 boy. Assuming the probability of having a girl is the same as the probability of having a boy (both .5), test events A and B for independence if (A) The family has 2 children. (B) The family has 3 children. 36. An experiment consists of tossing a coins. Let A be the event that at least 2 heads turn up, and let B be the event that all the coins turn up the same. Test A and B for inde- pendence if (A) 2 coins are tossed. (B) 3 coins are tossed. Problems 37-40 refer to the following experiment: 2 balls are drawn in succession out of a box containing 2 red and 5 white balls. Let R; be the event that the ith ball is red, and let W; be the event that the ith ball is white. 37. Construct a probability tree for this experiment and find the probability of each of the events R, n R2, RinW2, Win R2, Win W2, given that the first ball drawn was (A) Replaced before the second draw (B) Not replaced before the second draw 38. Find the probability that the second ball was red, given that the first ball was (A) Replaced before the second draw (B) Not replaced before the second draw 39 Find the probability that at least 1 ball was red, given that the first ball was (A) Replaced before the second draw (B) Not replaced before the second draw 40. Find the probability that both balls were the same color, given that the first ball was (A) Replaced before the second draw (B) Not replaced before the second draw