Question

Break-A-Leg Insurance Company sells a​ $500,000 insurance policy to thespians for​ self-inflicted lower-body extremity injury. The premium for the policy is​ $150 per year. If the probability that an actor actually breaks their leg and is paid​ $500,000 is​ 0.0001, compute the expected value the insurance company should expect to receive per policy sold.

Answer 1

Let x be the net profit or loss to insurance company and P(x) be the probability respectively.

Given : premium of the policy = $150 , Principle amount =$500,000

So Net profit to insurance company = $150

Probability that insurance company makes profit  = Probability that an actor do not breaks their leg = 1-0.0001= 0.9999

Net loss to insurance company = $500,000-$150 = 499850

loss represented by negative value , so Net loss = -$499850

Probability that insurance company occur loss = Probability that an actor actually breaks their leg = 0.0001

Expected value = ( Probability of profit *Net profit ) + ( Probability of loss *Net loss )

= ( 0.9999*150 ) + ( 0.0001*-499850)

=100.015

The expected value the insurance company should expect to receive per policy sold is $100.015