## Related questions with answers

For an extra $49 you can buy extended warranty protection on your new HDTV for three years. If the set requires maintenance during that lime, it will be free You estimate that there is a 5% chance that you might need a$300 repair within three years and a 1% chance that you will need a $500 repair, but the chances arc 94% that you will need no repair at all. Based on expected values, should you purchase the extended coverage?

Solution

Verified5% of the customers require a $\$300$ repair, while the extended warranty costs $\$49$ and thus a profit of $\$300-\$49=\$251$ is then made.

$P(\$251)=5\%=0.05$

1% of the customers require a $\$500$ repair, while the extended warranty costs $\$49$ and thus a profit of $\$500-\$49=\$451$ is then made.

$P(\$451)=1\%=0.01$

94% of the customers do not require a repair, while the extended warranty costs $\$49$ and thus a loss of $\$49$ is then made.

$P(-\$49)=94\%=0.94$

The expected value (or mean) is the sum of the product of each possibility $x$ with its probability $P(x)$:

$\begin{align*} \mu &=\sum xP(x) \\ &=\$251 \times 0.05+\$451\times 0.01+(-\$49)\times 0.94 \\ &=-\$29 \end{align*}$

Thus we are expected to make a loss of $\$29$ when purchasing the extended coverage, which implies that we should not purchase the extended coverage.

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