You buy a cell phone for $115 and there is a 5% chance that it will fail. You ca

Question

You buy a cell phone for $115 and there is a 5% 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 $115 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.

(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.

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

Explanation / Answer

b)  expected value for the cost of this phone =$120.75

c)Yes, because the expected cost is less than the cost of the phone plus the warranty

Outcomes          cost = x          Probability = P(x) xP(x) It fails     230 0.05 11.5 It doesn't fail     115 0.95 109.25 total 120.75

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