 Our full decision theory relies on two functions then, \(p\) and \(u\). The probability function \(p\) reflects how likely you think the various possible outcomes of an action are to obtain, while \(u\) represents how desirable each outcome is. Faced with a choice between two possible courses of action, \(A\) and \(\neg A\), with two possible states the world might be in, \(S\) and \(\neg S\), there are four possible outcomes, \(O_1,\ldots,O_4\). For example, if you bet $1 on a coin-flip coming up heads and it does comes up heads, outcome \(O_1\) obtains and you win $1; if instead it comes up tails, outcome \(O_2\) obtains and you lose $1. The general shape of such situations is thus: