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4 Tutorials that teach Theoretical Probability/A Priori Method

# Theoretical Probability/A Priori Method

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Author: Sophia Tutorial
##### Description:

This lesson will introduce the theoretical definition of probability.

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Tutorial

This tutorial will discuss the Theoretical Probability Model (aka a priori method) by focusing on:

1. Theoretical Probability Model
2. Unlikely Equal Outcomes

## 1. THEORETICAL PROBABILITY MODEL

A fairly common way to thinking about probability is to enumerate all the outcomes and assign them each an equal probability.

IN CONTEXT

Rolling dice. When you roll a die, there are 6 results since they are numbered: one, two, three, four, five, or six. Those are the outcomes.

Suppose you wanted the probability of rolling a two. Only one of those faces shows a two and there are six total faces, and so the probability of you rolling a two is therefore one out of six.

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.

Other probabilities calculated using this method are based on the key idea that outcomes are equally likely. Anytime you have outcomes that are equally likely,the theoretical probability method can be used. Such as:

• A coin flip
• Drawing a card from a deck (the deck must be adequately shuffled)
• Selecting marbles from a jar (all marbles must be equal size so you have an equal probability of picking them out). They should also be well mixed.

• Theoretical Probability
• The method of assigning probability to events based on the assumption that all events are equally likely. The probability of an event is the equally likely ways an event can occur divided by the number of possible outcomes.

• Theoretical Probability

## 2. UNLIKELY EQUAL OUTCOMES

The theoretical probability model does not work if the outcomes aren't equally likely.

You could use this reasoning to say something like you could get home safely from work in you car or you could get in a horrible car crash.

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 equal probabilities are not assigned in this case because experience shows that those two outcomes are not equally likely.

The theoretical probability model is also called "priori method", which means it's known prior to, or beforehand?

And so to recap, the Theoretical Probability Model 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. It does not work when the outcomes are unlikely equal.

Good luck!

Source: This work is adapted from Sophia author jonathan osters.

Terms to Know
Theoretical Probability

The method of assigning probability to events based on the assumption that all events are equally likely. The probability of an event is the equally likely ways an event can occur divided by the number of possible outcomes.

Formulas to Know
Theoretical Probability