Darwin Head, a 35-year-old sawmill worker, won $l million and a Chevrolet Malibu Hybrid by scoring 15 goals within 24 seconds at the Vancouver Canucks National Hockey League game (B. Ziemer, "Darwin Evolves into an Instant Millionaire," Vancouver Sun, February 28, 2008, p. 1). Head said he would use the money to pay off his mortgage and provide for his children, and he had no plans to quit his job. The contest was part of the Chevrolet Malibu Million Dollar Shootout, sponsored by General Motors Canadian Division. Did GM-Canada risk the $1 million? No! GM-Canada purchased event insurance from a company specializing in promotions at sporting events such as a half-court basketball shot or a hole-in-one giveaway at the local charity golf outing. The event insurance company estimates the probability of a contestant winning the contest, and for a modest charge, insures the event. The promoters pay the insurance premium but take on no added risk as the insurance company will make the large payout in the unlikely event that a contestant wins. To see how it works, suppose that the insurance company estimates that the probability a contestant would win a Million Dollar Shootout is 0.001, and that the insurance company charges $4,000.
a. Calculate the expected value of the profit made by the insurance company.
b. Many call this kind of situation a win-win opportunity for the insurance company and the promoter. Do you agree? Explain.