**3.1 Basic Concepts of Probability & Counting**

**Important Definitions**

Probability Experiment - An action, or trial, through which specific results are otained, like counts, measurements, or responses.

Outcome - The result of a single trial in a probability experiment.

Sample Space - The set of ALL possible outcomes of a probability experiment.

An Event - This is a subset of the sample space. It could be one or more outcomes.

Here's a simple example:

Your probability experiment is "rolling a 6-sided die".

The Sample Space is {1, 2, 3, 4, 5, 6}

An Event could be "rolling an even number" or {2, 4, 6}.

Your outcome could be "you roll a 2".

You will be finding the probability of an EVENT.

Events are often represented by uppercase letters, such as A, B, or C, but can also be represented by words, like "Ace", "Face Card", or "Odd Number".

A SIMPLE EVENT is an event that has exactly one outcome.

One way to find your sample space is to create a tree diagram.

The previous video mentioned "The Fundamental Counting Principle", let's talk a little more about that.

The Counting Principle basically says that if one event can occur "m" ways and another event can occur "n" ways, the the total number of ways they can occure in sequence is "m times n".

Here are a couple of examples that use the Fundamental Counting Principle

Don't you wish those guys in the last video were your stats teachers?

There are 2 types of probability . . .

1. Classical or Theoretical Probability is used when each outcome in a sample space is equally likely to occur. This is the type of probability that you've seen for years.

For example: What is the probability that you flip a coin and get tails. OR What is the probability that you choose a card from a deck and it is a face card?

2. Emperical or Statistical Probability is based on observations obtained from a probability experiment.

A lot of times you will be given a table or chart when faced with Emperical or Statistical Probability.

The Law of Large Numbers says that as an experiment is repeated, the emperical probability will approach the theoretical probability.

There is a 3rd type of probability called SUBJECTIVE probability.

This is based on intuition or educated guesses. For instance, a business analyst may predict that the chance of the employees of a certain company going on strike is 25%.

We will very rarely find subjective probability, but you should be able to identify it when you see it.

By the way, probabilities cannot be less than zero or greater than 1.

Complementary Events

The COMPLEMENT of an event is the set of all outcomes in a sample space that are NOT included in the event.

The COMPLEMENT of event E would be denoted as E', read as "E prime".

For example, if the event were rolling an even number on a die, then the complement would be NOT rolling an even number on a die.

Lastly, the only way to get better at probability is to practice the right way. So please take your practice problems seriously and

ask a lot of questions. This is the most difficult part of the course.

See you in stats class . . .