Answered by Lucas Curtis on Quora.

There’s a bit of confusion between

*probability*and

*odds*.

The

*probability*that an event will happen is the number of times you expect to see the event happen in many trials. For example, the probability of flipping heads on a fair coin is 0.5 (50%) because there is

*one*desired outcome (heads) but

*two*possibilities (heads or tails); ergo, you expect the desired outcome half the time.

The

*odds*that an event will happen is the ratio between the probability that an event

*will*occur, and the probability that it

*won’t*. So, the

*odds*in favor of flipping heads on a fair coin is one to one, because there are equal probabilities that you will and won’t land on heads.

So, let’s say that an event has a

*probability*of 0.003 (.3%). That means that in 1,000 trials, you expect the event to happen three times.

That means you expect it

*not*to happen 997 times. Therefore, the

*odds*against the event happening are 997 to three, or approximately 332 to one.