# Probability Basics

Base Definitions** Experiment** is a controlled operation that yields a set of results

**is each individual result**

*Outcome***is a collection of the results**

*Event***is when each outcome has the same chance of happening**

*Equally likely outcomes*- For example, if I were to roll a fair 6-sided die, this would be my experiment. I could roll it 20 times, and record what it lands on each time, each of these would be my outcomes. My Event would be all the times it landed on 3.

** Probability** is the study of the chance a situation will occur. There are several types of probability, including:

is when the probability is calculated based on what is thought will happen based on equally likely outcomes, sometimes called Mathematical Probability.*Theoretical Probability*- Theoretical Probability is the Number of Outcomes favorable to the Event divided by the Total possible Outcomes., ie P(E) = N/T.
- Using the die above, the Theoretical probability would be P(3) = 1/6, since there is only 1 out of the 6 sides with a 3 on it.
is when the probability is calculated based on what has happened before, sometimes called Posterior Probability or Relative Frequency, although this last one is technically a little different.*Empirical Probability*- Empirical Probability is the Number of time the Event Occurred divided by the Total number of times the experiment was performed, ie P(E) = N/T.
- Again, using the die above suppose when I rolled the die it landed on 3, 7 times, the Empirical probability would be P(3) = 7/20, reminder, we often will be reducing the fraction or converting it to a percent.
often refers to a personal opinion of an event happening.*Subjective Probability*- For example, I have cats and I also knit with yarn. There is a high probability that when I sit down to knit, at least one of the cats with try to help me with the yarn.
- Probability will always be between 0 & 1, inclusive, i.e. 0 ≤ P(E) ≤ 1
- So the probability something won’t happen is 0, i.e. P(rolling 9 on a standard 6-sided die) = 0
- So the probability something will happen is 1, i.e. P(the sun will rise tomorrow) = 1
- The sum of all probabilities is 1
- The probability of something not happening is P(not E) = 1 – P(E)
- The probability an event happens at least once is P(E happens at least once) = 1 – P(E never happens)

The following video goes over most of the above definitions, and a couple of others, and is about 4.5 minutes.

The following video goes over Theoretical Probability, Empirical Probability, and Odds use of the Formulae and is about 4 minutes.

The above videos will be redone to be a video per main topic.