This tutorial discusses odds. Odds are one way of describing probability. It's another way that we haven't seen yet. We've seen mostly probability ratios, fractions, percents, things like that. Odds are another way of doing that and representing that.
Now with odds, it's a ratio that's expressed in the simplest integer terms. So you're not going to see something like 1, 2, 3.5. Instead of that, we would have 2:7. So it's a ratio and it's in simplest integer terms, so we have whole numbers here. We don't use decimals.
If you had something like 3:6 odds, that's not simplest terms. We would reduce that to 1:2.
Now, we're going to learn how to go back and forth between the odds and those probability ratios that we're more familiar with. So for example, if we want to find the odds from a probability ratio-- so if the ratio, and by ratio here we mean probability ratio-- is A over B, then the odds in favor are going to be A to B minus A. So let's look at this example.
First, here's our probability ratio, 1/4 chance of getting a club. There is one suit that's club out of the four clubs total. Or if you had started off with there's 13 clubs out of the 52, you would simplify down to 1/4. So here, we mark this. This is our A, and the 4 is the B.
So now if I wanted to find the odds in favor, I would start off with the A, still. So 1 to-- and then B minus A. So 4 minus 1 is 3. So there's a 1:3 chance of getting a club.
And now those are the odds in favor of getting a club. If I wanted to find the odds against getting a club, we would essentially flip it around. We would find that it is a 3:1 odds against getting a club.
Now let's look at moving the other direction. If I had the odds and I wanted to find a probability ratio from the odds in favor, I can also do the same kind of process, but work in reverse. So if I know the odds in favor are A:B, then the ratio is going to be A over A plus B.
So first, if you start with the odds against getting an Oscar, you'd want to flip that around to get the odds in favor. So we had 48:1 odds against getting an Oscar, and 1:48 odds in favor of getting one.
So now in order to find the probability ratio, I'm going to follow the formula that we have. So with my odds this, is A and this is B. So my ratio is going to be A, so 1 over B plus A, 48 plus 1, 49. And we can see that that's what I had in fact found out from before, that you have a 1:49 chance, 1 out of 49 chance of winning an Oscar.
So most of these examples involve the 1 in some places. That's not always going to be true, but it's easy enough to calculate when you follow the formulas that we have. This has been your tutorial on odds.