6. Two fair dice are rolled. Find the following conditional probabilities of rolling: Second die First die (1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (3,1) (2,1) (2,2) (3,2) (2,3) (2,4) (2,5) (2,6) (3,3) (3,4) (3,5) (3,6) (4,1) (4,2) (4,3) (4,4) (4,5) (4,6) (5,1) (5,2) (5,3) (5,4) (5,5) (5,6) (6,1) (6,2) (6,3) (6,4) (6,5) (6,6) a) a sum of 8, given that the sum is greater than 7. b) a sum of 6, given that each die shows the same number. c) each die shows the same number, given that the sum is 9. 7. Two cards are drawn at random without replacement from an ordinary deck, find the following conditional probabilities: a) the second card is a heart, given that the first card is a heart b) the second card is black, given that the first card is a club