1. What is probability?
Probability measures how likely an event is to occur. Its value ranges from 0 to 1.
The probability scale
A probability of 0 means an event is impossible. A probability of 1 means the event is certain.
Values between them describe different levels of likelihood.
For example, when a fair coin is tossed, there are two equally likely outcomes: heads and tails.
2. Outcomes, sample spaces and events
Before calculating probability, we need to understand what outcomes are possible.
Sample space
The sample space is the complete set of possible outcomes.
For a single coin toss, the sample space contains two outcomes: heads and tails.
Event
An event is an outcome, or collection of outcomes, that we are interested in.
For example, getting heads can be represented by:
3. The basic probability formula
When all outcomes are equally likely, probability can be found by comparing the number of favourable outcomes with the total number of possible outcomes.
Example: rolling a die
A standard die has six possible outcomes:
Suppose we want the probability of rolling a 4. There is one favourable outcome and six possible outcomes.
4. Try a probability experiment
Toss a virtual coin repeatedly and compare the experimental result with the theoretical probability.
Ready to experiment
The theoretical probability of heads is \(\frac{1}{2}\).
5. Test your understanding
Try each question before checking your answer.
Question 1: A fair coin is tossed once. What is the probability of getting heads?
Question 2: A standard die is rolled. What is the probability of rolling a 6?
Question 3: What is the probability of an impossible event?
Continue learning
Probability connects naturally with mathematics, statistics, data science, and eventually more advanced mathematical models.