1. (15pts). A fair six-sided die is tossed. Define the following events: • A is the event that the number rolled is even • B is the event that the number tossed is 3 or less. • C is the event that the number tossed is a 1 or a 2. (a) Describe the sample space and the given events as sets. (b) Find P(A), P(B) and P(C). (c) Are A and B independent? What about A and C? What about B and C? (d) Compute P(A ? B) and P(A^c ? B). (e) Compute P(B|A) and P(C|A).
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Sample Space (S) = {1, 2, 3, 4, 5, 6} Now, let's define the given events as sets: Event A (even numbers) = {2, 4, 6} Event B (numbers 3 or less) = {1, 2, 3} Event C (numbers 1 or 2) = {1, 2} Show more…
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