Question: Problem 3. E1, E2, F be events in a probability space with sample space S and probability law Pr()), where Pr(F) 0. Prove the

Problem 3. E1, E2, F be events in a probability space with sample space S and probability law Pr()), where Pr(F) 0. Prove the following statements: (a) Pr(E UE2|F) = Pr(E|F) + Pr(E2|F) Pr(EE2|F). (b) Pr(EF) Pr(E| E2F) Pr(E2|F) + Pr(E|EF) Pr(E|F). Problem 4. Assume two independent fair dice are thrown in the sense that all the 36 outcomes are equally likely. Define E as the event that the two dice show the same number. Let F denote the event that the first

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