Actuarial Outpost Expected value question
 Register Blogs Wiki FAQ Calendar Search Today's Posts Mark Forums Read
 FlashChat Actuarial Discussion Preliminary Exams CAS/SOA Exams Cyberchat Around the World Suggestions

 Probability Old Exam P Forum

#1
03-29-2018, 01:32 PM
 poissonmushroom Member SOA Join Date: Nov 2013 Location: Warren, MI Studying for P/1 College: University of Toledo - Alumni Favorite beer: Dogfish Head Sahtea Posts: 31
Expected value question

I'm using the Marcel Finan text for the P Exam and had a question regarding a problem I'm trying to solve. The specific problem is 15.12. It reads:
A computer store specializes in selling used laptops. The laptops can be classified as either in good condition or in fair condition. Assume that the store salesperson is able to tell whether a laptop is in good or fair condition. However, a buyer cannot tell the difference. Suppose that the buyers are aware that the probability of a laptop being in good condition is 0.5. A laptop in good condition costs the store $500 and a buyer is willing to pay$525 for it whereas a laptop in fair condition costs the store $200 and a buyer is willing to pay$300 for it.

a) Find the EV of a use dlaptop to a buyer who has no extra information.
b) Assuming that buyers will not pay more than their EV for a used laptop, will sellers ever sell laptops in good condition?
So I used the EV formula to find that 0.4*(525)+0.6(300)=$390 My logic is that a good laptop costs the buyer 525 and there is a 40% chance the laptop they buy will be good. And since every laptop is either good or fair, then there is a 60% chance of the laptop being fair and it would cost the customer However the book answer for A is$2400

Can anyone give me a hint as to how the answer is 2400?
__________________
"Philosophers have only interpreted the world in various ways; the point, however, is to change it." - Karl Marx
#2
03-29-2018, 02:01 PM
 nonactuarialactuary Member Non-Actuary Join Date: May 2008 Posts: 2,038

Quote:
 Originally Posted by poissonmushroom I'm using the Marcel Finan text for the P Exam and had a question regarding a problem I'm trying to solve. The specific problem is 15.12. It reads: A computer store specializes in selling used laptops. The laptops can be classified as either in good condition or in fair condition. Assume that the store salesperson is able to tell whether a laptop is in good or fair condition. However, a buyer cannot tell the difference. Suppose that the buyers are aware that the probability of a laptop being in good condition is 0.5. A laptop in good condition costs the store $500 and a buyer is willing to pay$525 for it whereas a laptop in fair condition costs the store $200 and a buyer is willing to pay$300 for it. a) Find the EV of a use dlaptop to a buyer who has no extra information. b) Assuming that buyers will not pay more than their EV for a used laptop, will sellers ever sell laptops in good condition?So I used the EV formula to find that 0.4*(525)+0.6(300)=$390 My logic is that a good laptop costs the buyer 525 and there is a 40% chance the laptop they buy will be good. And since every laptop is either good or fair, then there is a 60% chance of the laptop being fair and it would cost the customer However the book answer for A is$2400 Can anyone give me a hint as to how the answer is 2400?
Are you posting the whole problem? The question is worded kind of weird. I’m assuming “EV of a used laptop to a buyer” is referring to the expected price the buyer is willing to pay, so 0.5*525 + 0.5*300 = $412.50. I don’t see any way it could be$2400. Unless you’ve omitted critical details, the max price a buyer is willing to pay is $525, and because they know there are some ‘fair’ laptops in the mix, their expectation is lower.$2400 doesn’t make any sense unless you’ve omitted critical detail or the problem is asking for something different. Maybe something wrong with the text (e.g., you’re looking at 15.12 but pulling the solution for 15.13)?

Part b is more interesting. If buyers are only willing to spend $412.50 on a laptop, selling laptops in good condition doesn’t make sense. They’d be losing money on every sale (acquire it for$500, sell it for $412.50). Either way, this type of question doesn’t really match up with the style for exam P. You’d be more effective studying using the manuals out there specifically geared to the exam (e.g., Actex, ASM, etc.), which means a single question and a multiple choice answer. You don’t get questions with multiple parts until you start taking upper level exams. By the way, why are you using 40% chance the laptop will be good in your answer? Doesn’t the problem state “Suppose that the buyers are aware that the probability of a laptop being in good condition is 0.5?” Was that a typo in you copying the problem here? #3 03-29-2018, 02:44 PM  Michael Mastroianni SOA Join Date: Jan 2018 Posts: 29 It looks like the answer to 15.12a is listed as 2400 here which appears to be his 2008 version. The wording in the May 2018 Syllabus version is this: Quote:  Suppose that buyers are aware that the probability of a laptop of being in good condition is 0.4. A laptop in good condition costs the store$400 and a buyer is willing to pay $525 for it whereas a laptop in fair condition costs the store$200 and a buyer is willing to pay for \$300 for it. (a) Find the expected value of a used laptop to a buyer who has no extra information. (b) Assuming that buyers will not pay more than their expected value for a used laptop, will sellers ever sell laptops in good condition?
The solutions in the book are:

(a) $0.4\times \525+0.6\times \300=\390$

(b) $E[V]=\390<\400$ so none will be sold

The book makes the assumption that the store would not sell a laptop for any amount below its cost.
__________________
Michael Mastroianni, ASA
Video Course for Exam 1/P: www.ProbabilityExam.com

Last edited by Michael Mastroianni; 03-29-2018 at 02:48 PM..
#4
03-29-2018, 02:48 PM
 poissonmushroom Member SOA Join Date: Nov 2013 Location: Warren, MI Studying for P/1 College: University of Toledo - Alumni Favorite beer: Dogfish Head Sahtea Posts: 31

Quote:
 Originally Posted by Michael Mastroianni It looks like the answer to 15.12a is listed as 2400 here which appears to be his 2008 version. The wording in the May 2018 Syllabus version is this: The solutions in the book are: (a) $0.4\times \525+0.6\times \300=\390$ (b) $E[V]=\390<\400$ so none will be sold The book makes the assumption that the store would sell a laptop for any amount above its cost.
Okay, so my logic was correct and the answers in the manual were incorrect. Thank you! Just wanted to make sure I wasn't losing my mind or missing some critical detail.
__________________
"Philosophers have only interpreted the world in various ways; the point, however, is to change it." - Karl Marx