Question

1. The following information for an auto insurance decision tree analysis is available.

   Auto theft rate (non-recoverable/beyond repair)	0.05
   Cost of your automobile	$27,000
   Cost of such an insurance protection	$1,600
   Deductible (lost and/or damaged beyond repair)	$500

   	a.	the payoff for buying this insurance when car is not lost is $24,300
   	b.	the payoff for not buying this insurance when car is not lost is not $25,375
   	c.	the expected value for not buying insurance is not $24,300
   	d.	the expected value for buying insurance is $24,300
   	e.	the payoff for not buying this insurance when car is lost, not recovered and/or recovered beyond repair is not $1,350
   	f.	the payoff for buying this insurance when car is lost, not recovered and/or recovered beyond repair is not $1,305
   	g.	the difference between buying and not buying this insurance is not $1,065
   	h.	there are three states for each decision alternative in this problem.

Answer 1

The payoff table is following:

	Car lost	Car not lost
Probability	0.05	0.95
Buy	27000-1600-500 = 24900	27000-1625400
Not buy	0	27000

	Statement	TRUE/FALSE	Explanation
a.	the payoff for buying this insurance when car is not lost is $24,300	FALSE	Payoff is 27000-1600 = $ 25,400
b.	the payoff for not buying this insurance when car is not lost is not $25,375	TRUE	Payoff is $ 27,000
c.	the expected value for not buying insurance is not $24,300	TRUE	Expected value = 0*0.05+27000*0.95 = $ 25,650
d.	the expected value for buying insurance is $24,300	FALSE	Expected value = 24900*0.05+25400*0.95 = $ 25,375
e.	the payoff for not buying this insurance when car is lost, not recovered and/or recovered beyond repair is not $1,350	TRUE	The payoff is $ 0
f.	the payoff for buying this insurance when car is lost, not recovered and/or recovered beyond repair is not $1,305	TRUE	The payoff = 27000-1600-500 = $ 24,900
g.	the difference between buying and not buying this insurance is not $1,065	TRUE	The difference = 25650 - 25375 = $ 275
h.	there are three states for each decision alternative in this problem.	FALSE	There are two states - Car is lost, Car is not lost