Question

Part 2 of 2 - Part 2

Carlie needed a personal computer (PC) for school but her budget was tight, so she decided on a used machine. After some searching, she was down to two possibilities. One she had found in a national franchized computer store, where she could purchase the PC for $800 with a one-year guarantee. But she was intrigued by a second possibility: a local charity store was offering a used machine that had been donated (exactly the same model as in the store) for $500.

Carlie talked to a computer repair specialist, who said the principal problem with this model of PC was the hard drive, which was prone to failure: he estimated that half of the PCs of this model and age would require a new drive. He offered to test the computer and check the condition of the drive for $60. If the drive was no good, a new drive could be fitted for $300 and would be guaranteed for one year. He added a qualification that his testing was not perfect: about 25% of drives that passed his testing failed soon afterwards requiring a new drive ($300) plus a service charge of $100 for diagnosing the problem (a cost that has to be paid with the fitting of a new drive).

Please only enter an integer if a numerical answer is required.

Question 8 of 12 10.0 Points The expected cost of buying the second hand computer from charity is

Question 9 of 12 10.0 Points Carlie would be better off to buy the computer with a one-year guarantee for $800. True False Reset Selection

Question 10 of 12 10.0 Points Carlie would expect to save $  with the test before purchase.

Question 11 of 12 10.0 Points If the second hand computer passes the test, then its expected cost is $  .

Question 12 of 12 10.0 Points Carlie should A. buy the second hand computer only if it passes the test. B. buy the second hand computer without taking the test. C. still buy the second hand computer even if it fails the test. Reset Selection

Answer 1

8). Expected cost of buying the computer from the charity:

a). Price = 500

b). Testing price = 60

c). Expected cost of testing = 25% prob. that the testing was faulty (requiring a new drive + service cost) + 75% prob. that the testing is successful

= (25%*(300+100)) + (75%*0) = 250

Now, this can occur after testing so, the 2 conditions for testing are: drive was faulty and it was replaced for $300 + the expected cost of testing

Total expected cost = (a)+(b)+(c) = 500 + 60 + 250 = 810

Expected cost of buying the computer from charity is $810

9). True. Carlie would be better off buying the computer for $800 with one year gaurantee.

10). Carlie would be expecting the cost for the computer from the charity to be 500 + 60 + 150 = 710

(150 from the testing the drive 0.5*300 + 0.5*100 = 150 and expecting the test to be correct.)

So, she would be expecting to save 800-710 = $90

11). If the computer passes the test, then expected cost would be 500 + 60 + 100 = 660 (100 from the drive being good but expected cost of test being (0.25*400) + (0.75*0) = 100)

12). Carlie should buy the computer only if it passes the test. Option A.