Answered Essay: Hi! Pleae use Excel decision tree add-in, and show the work. Thank you! Carlie needed a personal computer (PC) for school but her budget was tight

Hi! Pleae use Excel decision tree add-in, and show the work. Thank you!

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

The expected cost of buying the second hand computer from charity is

Question 9

Carlie would be better off to buy the computer with a one-year guarantee for $800.

True

False

Question 10

Carlie would expect to save $ with the test before purchase.

Question 11

If the second hand computer passes the test, then its expected cost is $ .

Question 12

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.

Expert Answer

First, consider the following notation and write what is given in terms of probabilities –

IS = Event denoting Test pass
IF = Event denoting Test fail
S = Good hard drive
F = Bod hard drive

P(S) = P(F) = 0.50
P(F|IS) = 0.25 so, P(S|IS) = 0.75

Also, note that it is absurd to buy the charity computer if the test shows that the hardware is faulty. Applying Baye’s theorem, we find the P(IS) = P(IF) = 0.50

Prior Conditional Joint = Prior x Cond Posterior
P(S) 0.5 P(IS|S) 0.75 0.375 P(S|IS) 0.75
P(F) 0.5 P(IS|F) 0.25 0.125 P(F|IS) 0.25
P(IS) = 0.500
P(IF) = 0.500

With this information, the decision tree will be as following –

Q8.

The expected cost of buying the second-hand computer from charity (without testing) is $700

Q9.

FALSE because the cost to purchase from the store is $800 which is more than $700.

Q10.

Carlie would expect to save $0 with the test before purchase.

Q11.

If the second hand computer passes the test, then its expected cost is $660.

Q12

B. buy the second hand computer without taking the test.

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