Question

Dr. Gebhardt just upgraded her phone to an iPhone Xs (she previously had an iPhone 6) and paid $1149 for the phone. She didn't know if she should purchase insurance for her phone. You need to help her Dr. Gebhardt has created a table similar to Table 5.2 or 5.3 in your text based on the following probabilities of damage or loss when she does not have insurance (see Probability Table 1) There is a 30% likelihood that Dr. Gebhardt will not damage There is a 40% likelihood that Dr. Gebhardt will break her screen. Screen replacement costs $135 There is a 20% likelihood that Dr. Gebhardt will accidentally damages her phone and breaks the screen It will cost $525 to repair the damage and the screen replacement costs $135 There is a 10% likelihood that Dr. Gebhardt will lose her phone. She would buy a new iPhone XS as a replacement or lose her phone. i. ii. iv. Probability Table 1: Dr. Gebhardt does not have insurance Payoff (this are the costs I would have to pay to make my phone "100% whole" again) $0 (no damage =no costs to repair or replace) $135 to repair screen only $660 to repair screen and fix additional damage $1149 to buy a new phone Probability Probability х раyoff $0 $54 Item i. No damage ii. Break screen only 0.30 0.40 iii. Break screenadditional damage $132 $114.90 $300.90 This expected value means she expects to have to pay $300.90 to maintain her phone without insurance (between the probabilities of no damage, breaking my screen, causing additional damage, or losing her phone) 0.20 iv. Lose phone 0.10 Expected Payoff (Value) : For this question, you must determine if purchasing "Apple Care +" insurance for her phone is worth it for your instructor. "Apple Care "insurance terms and conditions: Price of insurance $199 Screen damage copay $29 Any other accidental damage copay $99 No coverage for theft of loss. Create a new probability table and calculate expected value for "Apple Care +" insurance ("total cost of а. insurance"). Think carefully how to account for the price of the insurance vs. the copays. You can use Probability Table 2 as a template. Probability Table 2: Dr. Gebhardt purchases "Apple Care +" Insurance Probability Payoff (this are the costs I would have to pay to make my phone "100 % whole" again) Probability х раyoff Item i No damage ii. Break screen only ili. Break screen additional damage iv. Lose phone Expected Payoff (Value) = Total Cost of Insurance b. Compare the expected value of Dr. Gebhardt to maintain her phone without insurance to the total cost of insurance. Should she buy insurance? Explain She buys insurance if (EV to maintain the phone without insurance) > (total cost of insurance). She foregoes insurance if (EV to maintain the phone without insurance)

Answer 1

a) The probability of each of the item remains the same whether Dr. Gebhardt buys the insurance or not.

the probabilities for table 2 is below

Item	Probability
i. No Damage	0.30
ii. Break screen only	0.40
iii. Break screen + additional damage	0.20
iv. Lose phone	0.10

Next we will calculate the pay off for each of the events, if the instructor purchases "Apple care +" for $199

1. No damage = $0 (no damage hence no cost to repair or replace)
2. Break screen only= $20 for screen damage copay  
3. Break screen + additional damage = ($20+$99=$119) (screen damage copay + any other accidental damage copay)
4. Lose phone = $1149 (cost to buy a new phone as there is no coverage)

The expected payoff is calculated in the following table. The total cost of insurance is the expected payoff + Price of insurance.

ans: a)

Item	Probability	Payoff (These are the costs I would have to pay to make my phone "100% whole" again	Probability x payoff
i. No Damage	0.30	$0 (no damage hence no cost to repair or replace)	$0
ii. Break screen only	0.40	$20 for screen damage copay	$         8.00
iii. Break screen + additional damage	0.20	$20+$99=$119 (screen damage copay + any other accidental damage copay)	$       23.80
iv. Lose phone	0.10	$1149 (cost to buy a new phone as there is no coverage)	$     114.90
		Expected Payoff (Value)	$146.70
		Total Cost of Insurance	$345.70

Total cost of insurance = expected Payoff + Price of insurance = 146.70+199=345.70

b) The expected value of Dr. Gebhardt to maintain her phone without insurance is $300.90

The total cost of insurance for Dr. Gebhardt is $345.70

ans: She should forego the insurance as EV to maintain the phone without insurance is less than the total cost of insurance