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Question: a certain illness has two symptoms associated with it ...

Question details

A certain illness has two symptoms associated with it - a fever and fatigue. There is a 90% probability that at least one of the two symptoms occurs for a randomly selected person with the illness. There is an 80% probability that a randomly selected person with the illness will come down with a fever and there is a 50% probability that a randomly selected person with the illness will feel fatigued.

Please answer the following three questions:
1) Are the events of "fever" and "fatigue" mutually exclusive (or disjoint)?
2) Are the events of "fever" and "fatigue" complementary?
3) Are the events of "fever" and "fatigue" independent?

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