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Relative Frequency Probability/Empirical Method

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This tutorial covers two ways of calculating probability. It talks about the relative frequency probability method and also the subjective method. We're going to start with the relative frequency probabilities. Now, it goes by several other names. It's also known as experimental probability and the empirical method.

I'm going to use the word experimental probability the most often, but any of these terms refers to the same thing. And what is it referring to? It's referring to the probability you find when you're actually doing something when you're experimenting with it. And I don't necessarily mean beakers and test tubes in a science lab experimenting. I mean running a trial.

And as a review, a trial is talking about each occurrence of a random event-- each test, each flip of the coin, each roll of the die, each draw the card. So when we're talking about trials, we're talking about each action we're taking. So now the empirical method, the experimental probability, is talking about the ratio of the trials. And you're taking the ratio of the trials where the event that you're looking at occurs and dividing by the total number of trials.

Typically, this is done over the long run. You don't do it just once and then declare that to be the experimental probability. You repeat the same action over and over again and take the experimental probability of all of those times. So for example, off the top, we have a reminder here. We're doing the ratio of the number of trials and event happens to the total number of trials. And a fraction is one way of recording a ratio.

In the first example and the second example, we're talking about rolling a die. So I have a dice simulator here, and I'm going to record the roles that we get, because I'm actually rolling the die. This is just a way you could see it. So first, we're randomly rolling and we get a 1. Then we roll again and get another 1. I'm going to do this a couple times.

Now, I have six trials recorded, six times of rolling the die. And I got my results here. I get 1, 1, 4, 2, 1, 3. So the theoretical probability of getting any number is going to be different from our experimental probability. In theory, if I roll the die six times, I should get a 1 one of those times, a 2, a 3, a 4, a 5, and a 6. So I should have a 1/6 probability for any number.

Here, when we're doing experimental, we're saying, from what I actually rolled, how many times did a 2 come up? And a 2 came out once. And then how many total trials were there? There were six. Now, if instead, I said, what's the theoretical-- sorry-- experimental probability-- so what's the experimental probability of rolling a 1? The experimental probability for a 1-- there's one, two, three times it came up out of the six trials total.

So for a 1, it's going to be 3/6. And that's OK that it's different from the theoretical probability. Our next one says rolling even number. So we had one even number, two even numbers-- so two even numbers out of the six total. So in both of those cases, we're looking at our trials in order to determine our experimental probability.

We're going to do some examples now with cards, so I'm just going to get the dice information out of the way and switch to cards. All right, so now that we're talking about cards, I have a simulator for drawing a card from a deck. So instead of having a deck of cards in my hands and flipping up a card, I'm going to punch the button on the screen so that everybody can see.

So we're going to roll-- sorry-- we're going to deal out another card. And it's a nine of clubs. And I'm going to write out clubs, since I can't draw that well. Then it's a jack of spades, a seven of spades, a six of spades, another nine of clubs, a queen of hearts, two of hearts, a nine of spades, and I'm going to stop there.

So ideally, with experimental probability, you'd be doing this a lot more times, but for the time we have, eight is good enough. So now, what's the probability of drawing a black card? And here we can list all the trials that happened, the outcomes from that. And we have one, two, three, four, five, six, seven, eight trials total, so that's going to be our denominator.

And the number of times it was black-- one, two, three, four, five, six-- six out of eight-- that's our experimental probability from this set of data for forgetting a black card. Now, the probability of drawing a diamond-- we didn't get any done, so our probability of drawing a diamond here is zero out of eight. So that's our experimental probability.

So this tutorial had a coverage on experimental probability. It's what you get from actually conducting a set of trials. Now we'll talk about subjective probability. Subjective probability is not one that gets a lot of coverage in stats. It's not based on hard facts, and numbers, and data. It's based instead on what the subject thinks and the personal observation.

So it gets more commonly studied in psychology or behavioral economics-- things that's evaluating how people think. So an example is if someone says, I have a 50% chance of getting the job I interviewed for. They have no real reason to believe that it's 50% and not 60%, or 55%, or 75%. They're just taking a guess and basing it on what they think.

Similarly, if someone says, I'm certain that my baby will be a girl, even though they're not giving a percent here, this word certain-- we learned before that this links to the idea of 100%-- or a 1. So even though they haven't given you a number, it's still a probability because that certainty links to an idea of probability. So this is still a subjective statement because it's not based on fact. It's just based on what the person thinks. So this has been your tutorial on experimental probability and subjective probability.