Delta College\'s campus police are quite concerned with ever-growing weekend par

Question

Delta College's campus police are quite concerned with ever-growing weekend parties taking place at the various dormitories on the campus, where alcohol is commonly served to underage college students. According to reliable information on a given Saturday night one may observe a party to take place 67% of the time. Police Lieutenant Shark usually receives a tip regarding student drinking that is to take place in one of the residence halls the next weekend. According to Officer Shark, this tipster has been correct 43% of the time when the party is planned. The tipster has been also correct 74% of the time when the party does not take place. (That is, the tipster says that no party is planned.) If Officer Shark does not raid the residence hall in question at the time of the supposed party, he loses 15 career progress points. (The police chief gets complete information on whether there was a party only after the weekend.) If he leads a raid and the tip is false, he loses 80 career progress points, whereas if the tip is correct, he earns 100 points. Certainly he could raid always, or never, or do the opposite of what the tip says. (a) What is the probability that no party is actually planned even though the tipster says that there will be a party? The probability that no party is actually planned even though the tipster says that there will be a party is 0.09 . (Round to two decimal places.) (b) If the lieutenant wishes to maximize his expected career progress points, what should he do before getting any tip? Choose the correct answer below. y Raid the dormitories O Do not raid the dormitories (c) What is the EVPI (in terms of career points)? The EVPl is 26 points. (Round to the nearest whole number.)

Explanation / Answer

Solution-

Let the events are -

A: party is there

B : party is not there

T: Tipster is correct

F: Tipster is wrong

Given probabilities are -

P(A) = 0.67 and P(B) = 0.33 , P(T|A) = 0.43 P(T|B) = 0.74

(a) Required probability = P(F|B) = 1 - P(T|B)

= 1 - 0.74

= 0.26

(b) P(T) = P(A) * P(T|A) + P(B)*P(T|B)

=0.67 * 0.43 + 0.33 * 0.74

= 0.5323

So this is greater than being incorrect, so he should raid.

(C) EPV = -15 * P(F|A) - 80* P(F|B) + 100* P(T|A)

= -15 * ( 1- 0.43 ) - 80 * ( 1-0.74) + 100 * 0.42

= 12.65

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