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Probability of computers failing in 3 years

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Probability of computers failing in 3 years [#permalink]

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New post 08 Dec 2017, 22:48
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You are in charge of acquisition computers for 100 employees of your company on January 1, one computer for each employee. The computers are expected to serve for three calendar
years before they are retired and donated to a local school. Suppose each computer fails in each calendar year independently with probability 3%. If a computer is acquired in one calendar year and fails in the same calendar year, it is replaced by the vendor for free. If a computer is acquired in one calendar year and fails in a later calendar year, a new one is purchased to replace it right away. A replacement is treated the same as the one it replaces, and may or may not fail in the next year. The purchasing price of a computer is always $1,000. Due to inflation and technological
advances, the price is discounted by a factor of 0.9 each year, meaning the same computer costs 0.9*$1,000 (in today's money) to replace anytime in the second year, and only
0.9*0.9*$1,000 (in today's money) to replace anytime in the third year. From now on, all dollar amounts are in today's money.

a. What is the expectation of the total replacement cost (in today's money) for all 100 computers in the next three years?
b. If you just budget the amount you obtained in the preceding question, there is a good chance you will run into deficit. On the other hand, if you budget $500 per employee, you are likely to use only a small portion of it. Suppose you wish to budget for the least amount that is needed so that with probability 97.5% you have just enough. How much do you need to budget for?
c. The vendor offers a 3-year warranty at $99 per computer. If you purchase the warranty, any failed computer will be replaced at no additional cost. Would you take the offer?

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Re: Probability of computers failing in 3 years [#permalink]

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New post 10 Dec 2017, 08:02
ajaysuburbs wrote:
You are in charge of acquisition computers for 100 employees of your company on January 1, one computer for each employee. The computers are expected to serve for three calendar
years before they are retired and donated to a local school. Suppose each computer fails in each calendar year independently with probability 3%. If a computer is acquired in one calendar year and fails in the same calendar year, it is replaced by the vendor for free. If a computer is acquired in one calendar year and fails in a later calendar year, a new one is purchased to replace it right away. A replacement is treated the same as the one it replaces, and may or may not fail in the next year. The purchasing price of a computer is always $1,000. Due to inflation and technological
advances, the price is discounted by a factor of 0.9 each year, meaning the same computer costs 0.9*$1,000 (in today's money) to replace anytime in the second year, and only
0.9*0.9*$1,000 (in today's money) to replace anytime in the third year. From now on, all dollar amounts are in today's money.

a. What is the expectation of the total replacement cost (in today's money) for all 100 computers in the next three years?
b. If you just budget the amount you obtained in the preceding question, there is a good chance you will run into deficit. On the other hand, if you budget $500 per employee, you are likely to use only a small portion of it. Suppose you wish to budget for the least amount that is needed so that with probability 97.5% you have just enough. How much do you need to budget for?
c. The vendor offers a 3-year warranty at $99 per computer. If you purchase the warranty, any failed computer will be replaced at no additional cost. Would you take the offer?


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Re: Probability of computers failing in 3 years   [#permalink] 10 Dec 2017, 08:02
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