Question

6.   One insurance program involves 8 subjects with an income 5000. they are going to pay a 3000 medical bill once they get sick
Question
If the probability of getting sick is 1 in 20, what is the expected value
If the 8 subject bear different risks, 5% for number 1 to 3; 10% for number 4 to 6 and 20% for number 7 to 8. the insurance premium is set at 330. can the insurance stay in business? Is there a death spiral?

Answer 1

1. Probability of getting sick = 1 in 20 = 1/20 = 5%

Expected value = Payment * probability= 3000*5% = 150 per subject = 1,200 for all 8 subjects.

2. Total probability:

Subject	Probability
1	5
2	5
3	5
4	10
5	10
6	10
7	20
8	20
Total	85

Medical bill pay = 3000*85% = 2,550 (Cummulative payout, if subject 1 can fall sick 5% probability, sub 8 can fall sicj 20%, total would be sum of all subjects. so there is 85% chance that atleast one person would fall sick)

Premium : 330*8 = 2,640.

Net income = 2,640 - 2550 = 90. The business doesnt incur any losses with the probabilities given.