Probability
This topic covers 5 learning steps, guiding your child from the basics through to confident problem-solving. Each step includes a worked example and adaptive practice questions.
What Your Child Will Learn
- Probability Scale
Place events on a scale from impossible to certain - Calculate Simple Probabilities
Find probability as a fraction of outcomes - Expected Outcomes
Calculate expected number of successes - Combined Events
Use sample spaces for two events - Challenge — Probability Problems
Complex probability problems in context
Before This Topic
Your child should be comfortable with:
- Equivalent Fractions (Year 4)
- Charts & Data (Year 4)
Common Mistakes
- Believing that past results affect future independent events (e.g. "I have flipped heads 5 times in a row so tails must be next")
Each coin flip is independent — the coin has no memory. The probability of tails is still 1/2 every single time, no matter what happened before. This mistake is called the gambler's fallacy. - Thinking probability must always be written as a percentage (and not as a fraction or decimal)
Probability can be expressed as a fraction (1/6), a decimal (0.1667), or a percentage (16.7%). In maths, fractions are often preferred because they are exact and easy to work with.
Tips for Parents
- Roll dice and tally the results: "If you roll a fair die 60 times, how many sixes would you expect?" (10, because 1/6 of 60 = 10). Then actually do it and compare.
- Use a bag of sweets: "There are 3 red and 7 blue sweets. What is the probability of picking a red one?" 3 out of 10 = 3/10.
- Discuss the probability scale using everyday language: impossible (0), unlikely, even chance (0.5), likely, certain (1). Ask your child to place events on the scale.
- Play card games and ask probability questions: "What is the probability of drawing a heart from a full deck?" (13/52 = 1/4).
Key Words
- Probability — A number between 0 and 1 that describes how likely something is to happen — 0 means impossible, 1 means certain.
- Outcome — One possible result of an experiment — rolling a 4 is one outcome of rolling a die.
- Event — A set of outcomes you are interested in — "rolling an even number" includes the outcomes 2, 4, and 6.
- Sample space — The complete list of all possible outcomes — for a coin, the sample space is {heads, tails}.
- Expected outcome — The result you would predict based on probability — if P(heads) = 1/2 and you flip 100 times, you expect about 50 heads.
- Fair — When every outcome is equally likely — a fair die has a 1/6 chance for each number.
Where This Fits
Before this topic: Children should understand fractions, be able to simplify fractions, and have a basic sense of likelihood from everyday experience.
After this topic: Basic probability leads to combined events, tree diagrams, Venn diagrams, conditional probability, and statistical reasoning at GCSE.
How MathCraft Teaches This
In MathCraft, Probability is taught through the Coordinates & Statistics adventure track. Your child follows guided lessons with friendly characters, works through examples step by step, then practises with questions that adapt to their level.
The adaptive engine tracks mastery across all 5 steps, revisiting concepts your child finds tricky and advancing when they're ready. Parents can see detailed progress in the Parent Dashboard.
Practise Probability with MathCraft
Step-by-step lessons, worked examples, and adaptive practice — all wrapped in an adventure game your child will love.
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