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PLEASE EXPLAIN WITH DETAIL DONT COPY AND PASTE ANSWERS Consider randomly selecting a student at a...

PLEASE EXPLAIN WITH DETAIL DONT COPY AND PASTE ANSWERS

Consider randomly selecting a student at a certain large university, and let A denote the event that the selected student has taken a course in Philosophy and let B denote the event that the student has taken an on-line course. Suppose that ?(?) = .5, ?(?) = .4, and ?(? ∩ ?) = .25.

a. Determine the probability that the selected student has taken either a Philosophy course or an on-line course.

b. Determine the probability that the selected student has taken either a Philosophy course or an on-line course but not both.

c. Determine the probability that the selected student has taken neither a Philosophy course nor an on-line course. d. Determine the probability that the selected student has taken a Philosophy course but has never taken an on-line course.

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