Explain how

(i) a risk-averse individual,
(ii) a risk-neutral individual, and
(iii) a risk-preferring individual would respond to the opportunity of placing a bet at fair odds.

(i) When faced with options that have the same expected value, a risk-averse individual prefers the basket of outcomes with the least amount of risk. If the individual is already in a risk-free situation, he will decline a bet at fair odds. If the individual is not in a risk-free situation, he will choose to bet at fair odds so that his income will not be affected by the state of the world.
(ii) A risk-neutral individual cares only about the expected value of a basket of outcomes, regardless of the amount of risk involved. When he has the opportunity to bet at fair odds, all possible wagers have the same expected outcome, so the individual is indifferent about the decision to bet.
(iii) When faced with options that have the same expected value, a risk-preferring individual prefers the basket of outcomes with the most amount of risk. Thus, when given the opportunity to bet at fair odds, he will wager everything on one outcome or the other.