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Of the students living in the dormitories at a university, 65% live at the west...

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Calculus

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Of the students living in the dormitories at a university, 65% live at the west hall, and the rest at the south tower. A sandwich shop randomly mails a coupon for a free sandwich to 21% of those at the west hall, and to 18% of those living at the south tower. Let D be the event that the person receive a coupon, E? be the event that the person is living in the west hall, and E? be the event that the person is living in the south tower. A student living in a dormitory is randomly chosen. Complete parts (a) through (c) below.a. Find the probability that this person received a coupon.Write an expression that models the probability. Choose the correct answer below.A. P(E?ID).P(D) + P(E?ID).P(D)B. P (DIE?).P(E?) + P(DIE?),P(E?)C. P (DIE?).P(E?)D. (P(DIE?) + P(E?)) (P (DIE?) + P(E?))The probability is(Do not round until the final answer. Then round to three decimal places as needed.)b. Find the probability that this person is from the west hall, given that this person received the coupon.Write an expression that models the probability. Choose the correct answer below.

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