probability vs odds

If the odds are 0.3 percent, why is it that they say it’s 330 to one? What’s the math behind this?

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.