Problem 1: Joint, Conditional, Marginal Probability Suppose we throw a fair six-sided die twice in a row. Let A be a random variable representing the number on the first throw, and B be the number on the second throw. Let S be the sum of both throws. What are the following probabilities? a) P(A=1, B = 2 |S = 3) b) P(S =3|A= 1, B = 2) c) P(A= 1, B = 2 | S = 4) d) P(A=1|S= 6) e) P(A=3|S = 6) f) P(A =1|S = 2) 9) P(S = 10) h) P(S = 6)

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