Warranty: You buy a cell phone for $110 and there is a 6% chance that it will fa
ID: 3231720 • Letter: W
Question
Warranty: You buy a cell phone for $110 and there is a 6% chance that it will fail. You can pay an additional $11 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 $110 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 ($11), did you make the right decision to not buy the warranty and why? There is only one correct answer and explanation.
Yes, because the expected cost is less than the cost of the phone plus the warranty.
No, because the expected cost is greater than the cost of the phone plus the warranty.
Yes, because the expected cost is greater than the cost of the phone plus the warranty.
No, because the expected cost is less than the cost of the phone plus the warranty
Outcomes cost = x Probability = P(x) It fails It doesn't failExplanation / Answer
a)In this case,We know that we have to pay for the first phone and that is fixed=110,Now if we dont buy warranty,we will have to pay for the second phone,if first one fails with probability 0.6 and we don't pay for second phone if don't fail with probability 0.4.
b) Expected cost of the phone =Cost of the first phone(fixed)+cost of second phone when first fail+cost of second phone when first does not fail
Expected cost of the phone=110+110*0.6+0*0.4=110+66+0=$ 176
c) Now compare the expected cost of the phone(when we do not buy warranty) and the cost of phone (when we buy phone with warranty)
Expected cost of the phone=$ 176(when we do not buy warranty and buy second phone if the first one fails)
Cost of phone when we buy phone with warranty=110+11=$121
Expected cost of the phone(when we do not buy warranty) > Cost of phone(when we buy with warranty)
Hence,it was not right decision to not buy the warranty.
So the below option is correct:
No, because the expected cost is greater than the cost of the phone plus the warranty.
Outcomes cost = x Probability = P(x) It fails 110 0.6 It doesn't fail 0 0.4Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.