In a carton of 12 eggs 5 are brown and 4 are cracked. Three of the brown eggs are cracked. Let X be the number of cracked eggs among 6 selected at random and without replacement from the carton. Let Y be the number of BROWN cracked eggs among the 6 selected. Find the marginal pmfs of X and Y, explore if X and Y are independent and find the conditional pmf of Y given that 3 eggs among the six selected are cracked. What is the probability that X<4 and Y<2? What is the probability that X>1?