Question

An electronics store offers an extended warranty on all devices that they sell. Under the extended warranty, the store will refund a customer the original price of a purchased device if it breaks during the first 3 years of ownership.

Carson is purchasing a new mp3 player from the electronics store for $83.87. The extended warranty on the mp3 player costs $6.69.

Suppose Carson knows that there is a 17% chance that his mp3 player will break in the next three years. If his mp3 player breaks, he intends to replace it with the same model. What should Carson do if he wants to minimize his costs?
A.
Carson should not purchase the extended warranty because the expected cost of purchasing the extended warranty is less than the expected cost of not purchasing the extended warranty.

B.
Carson should purchase the extended warranty because the expected cost of purchasing the extended warranty is less than the expected cost of not purchasing the extended warranty.

C.
Carson should purchase the extended warranty because the expected cost of purchasing the extended warranty is greater than the expected cost of not purchasing the extended warranty.

D.
Carson should not purchase the extended warranty because the expected cost of purchasing the extended warranty is greater than the expected cost of not purchasing the extended warranty.

Answer 1

@Vocaloid @Hero

Answer 2

@vannieduval check your messages

Answer 3

@Hero You never answered my question ;-;

Answer 4

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Hero
Let \(x\) be the expected cost of purchasing the extended warranty
and \(y\) be the expected cost of not purchasing the extended warranty
and \(z\) be the pobability the mp3 player will break during a given time period

Then, the above scenario can be represented by the following diagram:

\[\begin{array}{ |c|c|c|c| }
\hline
& x & y & z
\\ \hline
\le \text{3 years} & $90.56 & 2(83.87) = $167.74& 0.17
\\ \hline
> 3 \text{years} & $83.87 & 2(83.87) = $167.74 & 0.83
\\\hline
\text{Tot Exp Cost} & \small{90.56(0.17) + 83.87(0.83)} & \small{167.74(0.17) + 167.74(0.83)} &
\\\hline
\text{Sum} & $85.00 & $167.74
\end{array}\]

Thus \(x < y\)

@vannieduval Given the results of the given scenario, which answer choice best reflects what Carson should do?

Answer 5

b and c?

Answer 6

There can only be one correct answer.

Answer 7

Think carefully

Answer 8

A?

Answer 9

@Hero Is it a?