Question 1 110pts) A bag contains 10 identical red balls and 20 identical green balls. You draw 3 balls at random without replacement. a) What is the probability that you get no red balls? (3pts) b) What is the probability that you get exactly k red balls (Give an expression for k, no need to simplify)? (4pts) c) If we decide to write the letter \"A\" on 2 balls, \"B\" on 2 balls, and \"C\" on 1 ball. Each ball can only have 1 letter. In how many different ways can we write these letters for all 30 balls? (3pm) Question 2 glptsl Suppose we have 2 events, C and D, and we have P(C) = 0.4, P(C U D) = 0.7. a) If C and D are mutually exclusive, then P(D) =? (3pts) b) If C and D are independent, then P(D) 2? (4pts) 0) If C and D are independent, then P(CE) =? (3pts) Question 3 glOptsl Suppose X and Y are i.i.d. (independent and identically distributed) random variables and c, 0 S x S 3, ix (x) _ {0, otherwise. a) Calculate c. (Zpts) b) Derive the joint distribution function f(x, y) of X and Y. (2pts) 0) Calculate P(X2 + Y2