LESSON: Intro to Probability Notation
| Site: | Mountain Heights Academy OER |
| Course: | Introductory Statistics Q4 |
| Book: | LESSON: Intro to Probability Notation |
| Printed by: | Guest user |
| Date: | Saturday, 26 April 2025, 12:43 PM |
Probability Notation
This quarter we are going to be focussing our studies on Probability! What is probability you ask? It's simply how likely something is to happen. If we're unsure about the outcome of an event -- whether it be the outcome of a basketball game, flipping a coin, willing the lottery or passing your statistics class -- we can talk about the probabilities of certain outcomes and how likely they are. The analysis of probabilities is called statistics. That's why we learn about probability in a statistics course.Before we jump in to learning about probability, it's important that you become very comfortable with the notation that will be used. It looks different than what you're used to. And if you're not paying attention now, it will definitely look like a different language down the road.
In this lesson video you will see a basic probability example of drawing poker chips out of a bag. You will also see the proper notation to denote probabilities and be introduced to the operators $$\bigcup$$ (or), $$\bigcap$$ (and) and | (given).
Theoretical Probability
The type of probability problems that we've looked at so far use Theoretical Probability.
Theoretical Probability is used when each outcome is equally likely to occur. Written in probability notation we would say, to find the probability of an event E:
Let's see a few more common examples of theoretical probability in the following lesson video:
Intuitive Sense of Probabilities
What does a probability of 0 mean? What does a probability of 1 mean? These are the questions we will explore in the following lesson video:
Important Vocabulary
As I said before, probability can look like a whole new language at first! So it's important to learn the terms and symbols that we use in order to successfully understand this topic.
The following are the symbols and vocabulary words that will show up in our study of probability:
Probability: the likelihood that something will occurr
Theoretical Probability: a type of probability calculation that is used when all outcomes are equally likely to occurr
Outcome: the result of a single trial of an experiment
Event: a set of related outcomes
Mutually Exclusive Events: two events that cannot occur at the same time
Disjoint: describes two events that have a probability of 0 for occurring at the same time
$$\bigcup$$: in probability means "or" and is sometimes referred to as "union"
$$\bigcap$$: in probability means "and" and is sometimes referred to as "intersection"
| : in probability means "given"
P(A): translates to, "The probability of event A."
REVIEW: Simplifying Fractions
On your upcoming assignments involving probability, you will be expected to write your answers as SIMPLIFIED FRACTIONS. In other words, if you find the answer to a problem to be $$\frac{4}{8}$$, I would expect you to simplify that fraction and enter your answer as $$\frac{1}{2}$$.
If you don't remember how to simplify fractions, take a look at this short video posted below. If you need more practice simplifying fractions, then visit this site.