Problem

Given:

• High risk (H) and low risk (L) individuals are interested in health insurance

• There are 100 H individuals and 900 L individuals in the population

• The chance an H person gets sick is 5% and the cost of an H person being sick is $1 million

• The chance an L person gets sick is 1% and the cost of an L person being sick is $100,000

Determine:

(1) The expected cost of insuring a random person from the population before any selection effects occur.

(2) The fraction of sick people who are uninsured after accounting for selection effects.

(3) The fraction of medical expenses that are not covered by insurance after accouting for selection.