Question

3) Find the expected gain or loss for an insurance company, if a life insurance premium on a $100,000 policy is $400, and the chance of death during the term is .003. per ticket for a raffle with a grand prize of a $2000 television and two second prizes of a $250 mobile phone. A total of 1000 tickets were sold for $5 each.

Answer 1

a) Policy amount = $100,000 Probability of death = 0.003

The expected value of the amount the insurance company must pay on the event of the death = Policy amount * Probability of death = 100000*0.003 = $300

The premium on the above policy = $400

Therefore the expected gain for insurance company = $400-$300 = $100

b)

There are 1000 tickets and 1 grand prize (of $2000 worth TV) and 2 second prizes (of $250 worth mobile phone)

Probability of winning a grand prize = 1/1000 = 0.001

Probability of winning second prize = 2/999 (since we need to exclude the person who had won a grand prize)

Expected gift amount a ticket buyer can expect = 2000*(1/1000) + 250*(2/999) = $2.5005

Cost of ticket = $5

Therefore the expected loss for a ticket buyer = $5-$2.5005 = $2.4995