Statistics and Probability (Mathematics Curriculum)
What Is Probability?
Probability is a measure of how likely (how probable) an event is to happen.
Probability allows us to assign a number to the likelihood of an event: between 0 (impossible) and 1 (certain).
The Oxford English Dictionary defines a probability as "the extent to which a particular event is likely to occur... expressed by a number between 0 and 1.
Imagine the following events.
A pig flying is impossible. It has a probability of 0. It will happen 0 times.
The probability of tossing a Head from a coin toss is 1⁄2.
The probability of a fully grown elephant being heavier than a man is 1. It is certain. In every case, the elephant will be heavier than the man.
These are all examples of probability.
Where Does the Word Probability Come From?
Probability comes from the Latin word 'probabilis' meaning "provable, credible".
Probability is about assigning a number to how likely an event is to happen.
In this mini-curriculum, you will learn about the probability of events.
Probability is a measure of how likely (how probable) an event is to happen. A probability is expressed as a number between 0 (impossible) and 1 (certain).
Probabilities can be shown on a probability scale:
Find a Probability
To find the probability of an event, divide the number of ways an event can happen by the total number of outcomes.
For example, there is 1 way to get a Heads in a coin toss and 2 possible outcomes (Heads and Tails). The probability is 1⁄2.
We can find the probability of a single event, like tossing a Heads.
What about combined events? We might want the probability of more than one event. What if this and that happen? What if that or this happen?
In this mini-curriculum, you will learn about the probability of combined events.
An event is independent if its outcome does not affect the probability of other events occuring.
Coin tosses are independent events. The outcome of one toss does not affect the probability of the next event.
The multiplication rule is used to find the probability of one event and another event.
An event is dependent if its probability is affected by whether or not another event has occured.
Picking a card out of a pack without replacing it is a dependent event. Everytime a card is taken out, it affects how many cards there are to pick from.
Mutually Exclusive Events
Two or more events are mutually exclusive if they cannot happen at the same time.
A tossed coin cannot land as Heads and Tails at the same time. They are mutually exclusive events.
The addition rule is used to find the probability of one event or another event.
The complement of an event in probability is all outcomes that are not the event.
The complement of tossing a Heads is tossing a Tails
A tree diagram is a diagram which shows the possible outcomes of an event and their probabilities.
Each outcome is shown as a branch... which is why it is called a tree diagram.
In this mini-curriculum, you will learn about tree diagrams and how to use them to calculate probabilities.
A tree diagram shows all the possible outcomes of an event and their probabilities.
Draw a Tree Diagram
To draw a tree diagram, list the possible outcomes of an event, draw and label a branch for each outcome and write the probability for each outcome.
Multiplication Rule on a Tree Diagram
The multiplication rule on a tree diagram can be used to find the probability of one event and another event by multiplying along the branches.
P(Heads and Heads) = P(Heads) × P(Heads)
Addition Rule on a Tree Diagram
The addition rule on a tree diagram can be used to find the probability of one event or another event by adding across the branches.
P(Heads or Tails) = P(Heads) + P(Tails)