Of the students living in the dormitories at a university, 73% live at the west

ID: 3294702 • Letter: O

Question

Of the students living in the dormitories at a university, 73% live at the west hall, and the rest at the south tower. A sandwich shop randomly mails a coupon for a free sandwich to 25% o those at the west hall, and to 19% o those living at the south tower. Let D be the event that the ers rece ve a coupon be he event at the person is living in the west hall, and E2 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. 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.

Explanation / Answer

a. PRobability that the random person who is living in dormatory will win the coupon. As D, E1 and E2 is defined in the question.

We can say the P = P (D l E1) * P(E1) + P(D l E2) * P(E2) (OPtion A is correct)

P = 0.25 * 0.73 + 0.27 * 0.19 = 0.234

b. Here the condition is that person received a coupon, now we want to know is it from west hall.

As in the last question we have calculated the probability for a random person to get a coupon.

so Pr (West Hall l Person shall get a coupon) = Pr (West hall and Get a coupon) / Pr( Get a coupon)

= P (D l E1) * P(E1) / [P (D l E1) * P(E1) + P(D l E2) * P(E2)]

Option B is correct.

so the probability is P1 = 0.73 * 0.25/ (0.73 * 0.25 + 0.27 * 0.19) = 0.781

Pr ( South Tower l Didn't received the coupon) = Pr ( SOuth Tower and Didn't received the coupon) / Pr(Didn't received the coupon)

Pr(Didn't received the coupon) = 1 - Pr ( Received the coupon) = 1- 0.234 = 0.766

Pr ( South Tower and Didn't received the coupon) = 0.27 * (1 - 0.19) = 0.2187

so Pr ( South Tower l Didn't received the coupon) = 0.2187/ 0.766 = 0.286

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Of the students living in the dormitories at a university, 73% live at the west

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