Expected value and expected utility Assume again that your utility function is u (x) = √x. Compute (i) the expected value and (ii) the expected utility of the following gambles:

(a) G: You have a 1/4 chance of winning $25 and a 3/4 chance of winning $1.

(b) G* : You have a 2/3 chance of winning $7 and a 1/3 chance of winning $4. Another major advantage of the expected-utility framework is that it can be applied to decisions that do not involve consequences expressed in terms of dollars, lives lost, or the like. The expected-utility formula can be used quite generally, as long as it is possible to assign utilities to all outcomes. That is to say that expected utilities can be calculated whenever you have preferences over outcomes – which you do, if you are rational. Hence, expected-utility theory applies, at least potentially, to all decisions. The following exercises illustrate how expected-utility reasoning applies even when consequences are not obviously quantifiable.