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Theoretical Probability/A Priori Method

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Source: Quarter, image made by Author; Cards, created from public domain http://www.jfitz.com/cards/ Marbles, Creative Commons: http://4photos.net/en/image:142-170532-A_bowl_of_marbles_images

In this tutorial, we're going to learn about the Theoretical Probability Model. It's also called the a priori method, which means it's known prior or beforehand. So let's take a look.

One way of thinking about probability-- and this is actually fairly common-- is to enumerate all the outcomes and assign them each an equal probability. So an example of this would be rolling dice. So when you roll a die, one, two, three, four, five, or six are the outcomes. And so suppose I wanted the probability of rolling a two. Well, only one of those faces shows a two and there are six total faces, and so the probability of me rolling a two is therefore one out of six.

And the understanding here is that the faces-- one, two, three, four, five, and six-- are equally likely. This is the key. There are other events whose probabilities can be calculated using this method. Anytime you have outcomes that are equally likely, like coin flip, or drawing a card from a deck, or or marbles from a jar. Or bowl, in this case. All the marbles in this case should be equal size so you have an equal probability of picking them out. They should also be well mixed. Same with the cards, the cards should be well shuffled.

Now this doesn't work if the outcomes aren't equally likely. You could use this reasoning to say something like, well, I could get home safely from work in my car or I could get in a horrible car crash. Well, if you assign those equal likelihoods, then the probability of you getting into a car crash is one half, because there's only two outcomes. You either make it home safe or you get in a crash. But we know from experience that the outcome of not having an accident to so much more likely than the outcome of having an accident. So we don't assign those equal probabilities. The theoretical approach doesn't work here, because we know from experience that those two outcomes are not equally likely.

And so to recap, the Theoretical Probability or a priori model says that when you have equally likely outcomes in some kind of chance experiment, the probabilities that you can determine for events is calculated by taking the number of outcomes in the event divided by the total number of outcomes that are possible, with the caveat being that this only works when the events are equally likely or the outcomes are equally likely. So we talked about theoretical probability. Good luck and we'll see you next time.