Problem 5, 10 points Roll three (6-sided) dice. Use inclusion-exclusion to find the probability that at...

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Problem 5, 10 points Roll three (6-sided) dice. Use inclusion-exclusion to find the probability that at least one value of 2 appears. Hint: Consider A, to be the event that the ith dice shows a 2 for i 1,2,3. We want to find P(A1 UA2U A3) using PI.E. for 3 events. You can assume that each dice is fair, that is, P(A) 1/6, P(Ai n A) 1/6x 1/6-1/36 and P(An A2nA3) (1/6)3 1/216. For an easier solution, consider the complement of the event at least one 2 appears, which is the value 2 never appears Problem 6, 10 points Is it always true that, if and A and B are events (maybe overlapping, maybe disjoint), then P(A U B) P(A) P(B)? If yes, then give a short and simple reason why this is always true. If no, then give a counterexample, i.e., a situation in which P(A U

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