Question

Warranty: You buy a cell phone for $90 and there is a 6% chance that it will fail. You can pay an additional $3 for the hassle-free replacement warranty. This means if it fails you will get a free replacement.

(a) Suppose you do not buy the warranty but will buy a second one if the first one fails (we will assume this second one does not fail) and you will pay the full $90 for the second one. Complete the following table to assist in calculating the expected cost for this phone. Enter the probabilities to 2 decimal places.

Outcomes	cost = x	Probability = P(x)
It fails
It doesn't fail

(b) Use the table to calculate the expected value for the cost of this phone. Round your answer to the nearest penny.
$

(c) Considering the expected cost above and the price of the warranty ($3), did you make the right decision to not buy the warranty and why? There is only one correct answer and explanation.

Yes, because the expected cost is less than the cost of the phone plus the warranty.No, because the expected cost is greater than the cost of the phone plus the warranty.    Yes, because the expected cost is greater than the cost of the phone plus the warranty.No, because the expected cost is less than the cost of the phone plus the warranty.

Answer 1

Cost of cell phone = $90

Probability that it will fail = 6%=0.06

Probability that it will not fail = 1-0.06 =0.94

Cost of the hassle-free replacement warranty = $3

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if the phone does not fail : Net cost of the phone : x = $90 ;  probability that it does not fail = 0.94 i.e P(X=90)=0.94

if the phone fails ; another phone is bought : Net cost of the phone : x = 90+90=180 and probability that it does not fail = 0.06 i.e P(X=180)=0.06

Outcomes	cost = x	Probability = P(x)
It fails	180	0.06
It doesn't fail	90	0.94

Expected value for the cost of this phone : E(X)

Expected value for the cost of this phone = $95.40

Cost of the phone + Warranty = 93

Expected value for the cost of this phone > Cost of the phone + Warranty

(c) Considering the expected cost above and the price of the warranty ($3), did you make the right decision to not buy the warranty and why? There is only one correct answer and explanation.

No, because the expected cost is greater than the cost of the phone plus the warranty.