conditional probability

3.5. An urn contains 6 white and 9 black balls. If 4 balls are to be randomly selected without replacement, what is the probability that the first 2 selected are white and the last 2 black? 3.6. Consider an urn containing 12 balls, of which 8 are white. A sample of size 4 is to be drawn with replacement (without replacement). What is the conditional probability (in each case) that the first and third balls drawn will be white given that the sample drawn contains exactly 3 white balls? 3.7. The king comes from a family of 2 children. What is the probability that the other child is his sister? 3.8. A couple has 2 children. What is the probability that both are girls if the older of the two is a girl? 3.9. Consider 3 urns. Urn A contains 2 white and 4 red balls, urn B contains 8 white and 4 red balls, and urn C contains 1 white and 3 red balls. If 1 ball is selected from each urn, what is the probability that the ball chosen from urn A was white given that exactly 2 white balls were selected? 3.10. Three cards are randomly selected, without replacement, from an ordinary deck of 52 playing cards. Compute the conditional probability that the first card selected is a spade given that the sec- ond and third cards are spades. 3.11. Two cards are randomly chosen without replace- ment from an ordinary deck of 52 cards. Let B be the event that both cards are aces, let A, be the event that the ace of spades is chosen, and let A be the event that at least one ace is chosen. Find (a) P(BAJ) (b) P(BA)