Question

Warranty: You buy a cell phone for $100 and there is a 6% chance that it will fail. You can pay an additional $10 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 $100 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 ($10), 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

a) The following table completed:

Outcomes	Cost = X	Probability = P(X)
It fails	200	0.06
It doesn't fail	100	0.94

b) With the help of the table above,

Expected value of X = E(X) = X₁P(X₁) + X₂P(X₂)

E(X) = 200(0.06) + 100(0.94)

E(X) = 12 + 94 = 106

Therefore, the expected cost of the phone is $106.

Ans: $106  

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