Your company has recently revamped its health care insurance plan. You now have a choice of one of three plans as shown below:
Plan 1: The monthly cost is $32 and the insurer pays 90% of all expenses after you have paid the first $500 each year ($500 deductible).
Plan 2: The monthly cost is $5 and the insurer pays 90% of all expenses after you have paid the first $1200 each year ($1200 deductible).
Plan 3: The monthly cost is $24 and the insurer pays 70% of all expenses (no deductible).
You have gone back several years and examined past medical expenses and created the following probability distribution.
Annual Medical Expenses ($) 
Probability 
100 
0.15 
500 
0.30 
1500 
0.35 
5000 
0.15 
10000 
0.05 
Required:
a. Prepare a decision table representation of this problem.
b. Prepare a decision tree diagram model of this problem.
c. Calculate the expected annual cost for each of the three plans.
d. Which plan do you recommend from a minimum cost perspective?
Solution:
a. Decision table
Monthly cost 
Expenses 
Expected cost with probabilities 

Plan 1 
$32 
$500 
$1940 (10%) 
Plan 2 
$5 
$1200 
$1940 (10%) 
Plan 3 
$24 
$0 
$1940 (30%) 
b. Decision tree diagram
c. For the expected annual cost for each of the three plans, we need to first calculate the expected medical expenses
Expected medical expenses = 100*0.15 + 500*0.30 + 1500*0.35 + 5000*0.15 + 10000*0.05
Expected medical expenses = $1,940
Plan 1 = $32 (12) + $500 + (1  90%) ($1940) = $1,078
Plan 2 = $5 (12) + $1200 + (1  90%) ($1940) = $1,454
Plan 3 = $24 (12) + $0 + (1  70%) ($1940) = $870
d. Choose plan 3 since it has the lowest annual cost.
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