Question: Please show work. Consider the following probability space. .5' = {1, 2, 3,4, 5,6}, 1/18 if=1,3, or4 P({}) = 1/6 if i = 2 or

Please show work.

Consider the following probability space. .5' = {1, 2, 3,4, 5,6}, 1/18 if=1,3, or4 P({}) = 1/6 if i = 2 or 5 1/2 if= 6 a.) Verify that P is a valid probability function on S. b.) Let A = {1, 2,3}, and let E be the event of observing an even number. Calculate P(A), P(A U E), and P(A|E). (Remember: you can leave your answer as a sum or product of fractions. No need to simplify or calculate decimal values.)

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