When it comes to betting, the chance of winning or losing may be expressed as odds. If there are n equally likely outcomes and m of them result in a win, then the odds of winning are m:(n − m), read ‘‘m to n − m.’’ For example, suppose that a player rolls a die and wins if the number of dots appearing is either 1 or 2.

Since there are two winning outcomes out of six equally likely outcomes, the odds of winning are 2:4.

Suppose that a pair of dice is rolled and the player wins if it comes up ‘‘doubles,’’ that is, if the same number of dots appears on each die. What are the odds of winning?