Question

Warranty: You buy a cell phone for $90 and there is a 6% chance that it will fail. You can pay an additional $9 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 ($9), 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

P[ phone will fail ] = 6% = 0.06

P[ phone will not fail ] = 1 - 0.06 = 0.94

Cost of phone if it fails and one buys a new one = the actual cost of phone + cost of new phone*P[ 1st phone will fail ] = $90 + $90*0.06 = $90 + $5.4 = $95.4

Cost of phone if it does not fail = the actual cost of phone = $90

Outcomes	cost = x	Probability = P(x)
It fails	95.4	0.06
It doesn't fail	90	0.94

b) Expected value for the cost of phone = sum( cost*P(x)) = 0.06*$95.4 + 0.94*$90 = $5.724 + $84.6 = $90.324

c) 1st option is correct

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