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Relative Frequency Probability/Empirical Method

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In this tutorial, you're going to learn about the relative frequency probability method. It's also called the empirical method. And this is something that's sort of based on past experience. So, right here, we have a chart for coin flips. So we start here, where it says start. And if we flip heads-- I'm going to define heads as being a win-- we're going to go up the line. And if we flip tails, we're going to go down the next line to the next dot. What this is showing is it's showing the experimental probability of heads.

So, if we flip heads on the first trial, our experimental probability is 100%. If we flip heads on the next trial, it remains 100%. If we flip a tail, then it reduces all the way down to 66.6%, and et cetera. And we can keep flipping coins to see what happens. The next one was heads, the next one was tails. And we can simulate, sort of, the rest of what happens-- couple more coin flips, couple of more, couple of more, couple of more.

And so, what do you notice? The graph is pretty erratic here at the beginning, but it really does sort of start to settle down here towards the end. And where does it settle in? Right around 50%, right there. And the idea is the longer we ran this experiment, the closer this blue line would stay to this red line. If we kept on going forever, the blue and red would be indistinguishable.

And so the frequentest approach-- it's also called the relative frequency approach-- says that the probability of an event is the number of times it's occurred in identical trials, divided by the total number of trials. So in this case, we're saying that the probability of a coin coming up heads is 50%, not because there are two faces to the coin, but rather because heads has come up about half the time in repeated trials of coin flipping.

One additional way to talk about probability is-- we're going to mainly leave this to psychology folks to debate-- but it's called the subjective approach. And it's not a mathematical model like some of the others that we talked about, like the frequentest approach or the a priori model, which is talked about in greater detail in another tutorial. But it's based on your judgment, your overall how you feel about something.

So, explaining that, oh, I'm 90% certain I left the garage open. Now, what does that mean? Does that mean, you know, if we were using the frequentest approach, you would say, all right, well, that means that 90% of the times that you felt this way you left the garage open? It just doesn't really make a lot of sense. They're saying that they're more sure than not sure that they left the garage open.

And you hear words like this all the time. I'd say there's about a 50-50 chance I got the job. Again, what does that mean? About half the time you felt this way you ended up getting the job? This isn't a frequentest approach. This isn't any mathematical model. And again, there's a one in a million chance of surviving that kind of accident. Again, they're just saying that they don't think that that's very possible or very probable. They're not saying that there's been a million such accidents and only one person survived.

And so, to recap. The relative frequency model is the one that we're going to mainly use. And it deals with looking at the past to see, relative to the total number of experiments that I've done, how many of them came up with this particular event. So, the relative frequency is defined as the probability of the event. We also talked about subjective probability and how that's not really a probability, technically. But it's more how you feel about it. and we're going to leave that more to psychology to talk about. So, we talked about relative frequency probability and subjective probability. Good luck and we'll see you next time.