Section 2. Fun and Games 2.1 You are looking for a new apartment. There are two

Question

Section 2. Fun and Games

2.1 You are looking for a new apartment. There are two types of apartments in the city: Good (20%) of the apartments) and bad (80% of the apartments). You could live in either of them, but you would prefer a good apartment. More specifically, a good apartment is worth 600$ to you while a bad one is worth 500$ (the rent is 500$ for both, so you get a bonus of 100$ if you land a good one). Each time you visit an apartment you have to pay a fee of 20$ (subway, work time lost, etc.).

The first apartment you visit is a bad one. Given the above information

Explanation / Answer

Apartment type 1: Good, 20%, worth $600, rent $500 Apartment type 2: Bad, 80%, worth $500, rent $500 Cost of each visit = $20 The first apartment ha been visited already. It doesn't change the probability that the next apartment would be god or bad. a) Cost of visiting new apartment = $20. Hence, the Expected Profit = -20 (i.e., cost of visit) + 0.2*100 (i.e., probability of finding a good apartment * profit after finding a good apartment) + 0.8 * 0 (i.e., profit of bad apartment) = $0 Hence, we should try for at least one time. b) Expected profit in n attempts = -20* number of attempts (i.e. n) + profit in finding a good apartment in the 1st attempt * probability of finding a good apartment in the 1st attempt + profit in finding a good apartment in the 2nd attempt * probability of finding a good apartment in the 2nd attempt = -20n + (0.2)*100 + (0.8*0.2)*100 + (0.8*0.8*0.2)*100 + ... + 0.8^(n-1) *0.2*100 = -20n +20* (1-0.8^n)/(1-0.8) = -20n + 100 - 100*0.8^n which is decreasing, hence he should try just once. Hence, the optimum number of trials which will give us a the maximum profit is 1 = Answer

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.