Question

Find the odds for and the odds against the event rolling a fair die and getting a 4 comma a 5 comma or a 2.

a. The odds for the event are
nothing to
nothing.

Answer 1

The odds in favor are 3:3 which reduces to 1:1

There are 3 ways to get what we want, which is 4, 5 or 2. There are 3 ways to get what we don't want (1,3,or 6). So we list those two values as a ratio like so 3:3, which reduces to 1:1 after you divide both parts by 3.

Here's another example. If we wanted to know the odds in favor of rolling a 5 or 6, then the answer would be 2:4 which reduces to 1:2. This is because there are 2 ways to get what we want (rolling a 5 or 6) and 4 ways to get what we don't want (rolling either 1,2,3, or 4). The number of events we favor is listed first when it comes to "odds in favor" problems.