Please provide enough explanations, thank you so much. Delta College\'s campus p

Question

Please provide enough explanations, thank you so much.

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 60% 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 40% of the time when the party is planned. The tipster has been also correct 80% 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 10 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 50 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? (b) If the lieutenant wishes to maximize his expected career progress points, what should he do before getting any tip? (c) What is the EVPl (in terms of career points)?

Explanation / Answer

B.

As the chance of a party is 60% and of no party is 40%

Then the return without information is = 60%*100+ 40%*(-50) = 60-20 = 40 points.

So The best idea is to not wait for the prediction and raid each and every time, as the outcome is + 40

C. So

for EVWOPI = 40

EVWPI = 100

So EVPI = 100-40 = 60

Step 1 P1 P2 P3 Prob Party predicted Party not predicted 60% Party planned 40% 60% 40% No Party 20% 80% Step 2 P So effective prob is P1*P2 P1*P3 Effective Prob Party predicted Party not predicted Party planned 24.00% 36.00% No Party 8.00% 32.00% No party but party is predicted 8.00% 0.08 Ans A Step 3 O Outcome Party predicted Party not predicted Party planned 100.00 -10.00 No Party -50.00 0.00 Step 4 P*O Expected Value Party predicted Party not predicted Party planned 24.00 -3.60 No Party -4.00 0.00 EVWPI EV Total 16.40 EVPI Max Return - EV total (Without PI) Max Return 100 EVWPI 16.40 EVPI 83.60 Ans C

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