1.Expected Returns

Suppose you are betting on a horse race, and there are three horses. The information you have is that the probability of horse 1, horse 2, and horse 3 winning are 0.5, 0.3, and 0.2, respectively. There are three types of cards you can choose. Card 1 pays you 70 dollars if horse 1 wins, and 10 if horse 2 or 3 win. Card 2 pays you 80 dollars if horse 3 wins, and 25 if horse 1 or 2 win. Card 3 pays you 40 dollars if horse 1 wins, 50 if horse 2 wins, and 10 if horse 3 wins. (16 points)

(a)What is the expected value of card 1?(3 points)

(b)What is the expected value of card 2?(3 points)

(c)What is the expected value of card 3?(3 points)

Which card would you want to own? Does your risk attitude influence your choice, and why? [Hint: You can safely assume that the payments are relatively little compared to your income.]