What Is Probability? A Beginner's Guide

Probability is the branch of maths that deals with how likely something is to happen. It shows up everywhere in daily life, from weather forecasts to sports odds to deciding whether to bring an umbrella. In the Australian Curriculum, probability is introduced in primary school and builds steadily through high school, so getting the foundations right early makes a real difference.

This guide covers the basics that Year 7 and Year 8 students need to know.

What probability actually means

Probability is a number that measures how likely an event is to occur. It always falls between 0 and 1 (or between 0% and 100%).

• Probability = 0 means the event is impossible. For example, rolling a 7 on a standard six-sided die.
• Probability = 1 means the event is certain. For example, the sun rising tomorrow.
• Probability = 0.5 means the event is equally likely to happen or not happen. For example, flipping a fair coin and getting heads.

Most events fall somewhere between 0 and 1. The closer to 1, the more likely the event. The closer to 0, the less likely.

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The basic formula

For situations where all outcomes are equally likely, the probability of an event is:

Probability = number of favourable outcomes divided by total number of outcomes

This is sometimes written as P(event) = favourable / total.

Worked example 1: Rolling a die

What is the probability of rolling a 3 on a fair six-sided die?

There is 1 favourable outcome (rolling a 3) and 6 possible outcomes (1, 2, 3, 4, 5, 6).

P(3) = 1/6

As a decimal, that is approximately 0.167, or about 16.7%.

Worked example 2: Drawing from a bag

A bag contains 4 red marbles, 3 blue marbles, and 5 green marbles. What is the probability of drawing a blue marble?

Favourable outcomes: 3 (the blue marbles)

Total outcomes: 4 + 3 + 5 = 12

P(blue) = 3/12 = 1/4

That is 0.25, or 25%.

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Expressing probability

Probability can be written as a fraction, a decimal, or a percentage. Exam questions will sometimes specify which form they want, so students should be comfortable converting between all three.

Fraction	Decimal	Percentage
1/2	0.5	50%
1/4	0.25	25%
1/5	0.2	20%
3/10	0.3	30%
2/3	0.667	66.7%

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Key probability language

Understanding the vocabulary is half the battle in probability questions. Here are the terms students need to know:

• Experiment: The activity being performed (rolling a die, flipping a coin, drawing a card).
• Outcome: A single possible result (rolling a 4, getting tails).
• Sample space: The set of all possible outcomes. For a coin flip, the sample space is {heads, tails}. For a die roll, it is {1, 2, 3, 4, 5, 6}.
• Event: A specific outcome or group of outcomes you are interested in (rolling an even number, drawing a red card).
• Favourable outcomes: The outcomes that match the event you are calculating for.
• Complementary event: The opposite of an event. If the probability of rain is 0.3, the probability of no rain is 1 minus 0.3 = 0.7.

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Complementary events

One of the most useful ideas in probability is that the probability of something happening plus the probability of it not happening always equals 1.

P(event) + P(not event) = 1

This means if you know one, you can always find the other. For example, if the probability of picking a red marble from a bag is 1/3, then the probability of picking a marble that is not red is 1 minus 1/3 = 2/3.

This is especially useful when it is easier to calculate the probability of something not happening. If a question asks "what is the probability of rolling a number that is not 6?", you know P(6) = 1/6, so P(not 6) = 5/6.

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Experimental vs theoretical probability

There is an important distinction between two types of probability:

Theoretical probability is what you calculate using the formula above. It assumes everything is perfectly fair. The theoretical probability of heads on a fair coin is exactly 1/2.

Experimental probability is what you observe when you actually perform the experiment. If you flip a coin 100 times and get heads 47 times, the experimental probability of heads is 47/100 = 0.47.

The more times you repeat an experiment, the closer the experimental probability gets to the theoretical probability. This idea is called the law of large numbers, and it explains why flipping a coin 10 times might give you 7 heads (70%), but flipping it 10,000 times will give you something very close to 50%.

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Common mistakes to avoid

• Thinking past results affect future outcomes. If you flip heads five times in a row, the probability of heads on the next flip is still 1/2. The coin does not have a memory. This mistake is so common it has a name: the gambler's fallacy.
• Giving a probability greater than 1 or less than 0. If your answer is 5/3 or negative, something has gone wrong. Go back and check.
• Confusing "or" and "and" in compound events. "Rolling a 3 or a 5" is different from "rolling a 3 and then a 5." This becomes important in Year 9 and beyond, but it is good to be aware of early.
• Not counting the total outcomes correctly. In the marble example, the total is all the marbles, not just the colour you are interested in.

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Where to from here

The basics covered here form the foundation for more advanced probability topics that come in later years: two-step experiments, tree diagrams, Venn diagrams, and conditional probability. If the fundamentals are solid, those topics build naturally on top.

If your child is working through probability in class and would like some extra guidance, imSteyn covers probability as part of the Year 7 and Year 8 statistics and probability units. It uses a question-and-answer approach that helps students think through problems rather than just memorise rules. You can try it free to see if it suits your child's learning style.