11+ Probability
Learn the 0 to 1 probability scale, calculating single and combined event chances, expected frequency, and mutually exclusive outcomes for 11+ exams.
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Video lessons
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Untimed Probability Test
5 questions · drawn from 25 · no timer · unlimited retakesPractise calculating probability fractions, decimals, and percentages without time pressure.
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Timed Probability Test
5 questions · drawn from 25 · 5 minutes · unlimited retakesSharpen your rapid likelihood calculation and expected frequency speed under 5-minute timed exam conditions.
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Year 4 Probability Test
5 questions · drawn from 40 · no timer · unlimited retakesGentle introduction using everyday probability words (impossible, unlikely, evens, likely, certain).
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Interactive Probability Lab & Explorer
Interactive Practice · 3 ModulesExperiment with marble bags, coin tosses, and dice rolls in real time. Watch how outcomes translate directly into 11+ fraction, decimal, and percentage probabilities.
🎲 Probability Explorer 11+ Edition
The Marble Bag
💡 11+ Probability Facts
| Format | Value |
|---|
Change the Marbles
Target Colour
Possible Outcomes (1 Coin)
What are we looking for?
💡 Probability Rule
| Matching Outcomes | 0 |
| Total Possible | 0 |
| Fraction | 0/0 |
Possible Outcomes (1 to 6)
What are we looking for?
💡 Probability Fraction
| Matching Numbers | 0 |
| Total Possible | 0 |
| Fraction | 0/0 |
| Simplified | 0 |
Probability rules and exam techniques
Probability measures how likely an event is to happen. Express probabilities as fractions in lowest terms, decimals, or percentages.
The Probability Scale (0 to 1)
Probability is always a value between 0 (impossible) and 1 (certain). It is expressed as a fraction, decimal, or percentage.
| Likelihood | Value | Example Scenario |
|---|---|---|
| Impossible | 0 (0%) | Rolling a 7 on a standard 6-sided die |
| Unlikely | < 0.5 (< 50%) | Picking a heart from a deck (¼ or 25%) |
| Even Chance | 0.5 (50%) | Flipping Heads on a fair coin (½) |
| Likely | > 0.5 (> 50%) | Rolling a number greater than 1 on a die (⅚) |
| Certain | 1 (100%) | The sun rising tomorrow |
3 Golden Probability Rules
Master these exam rules to solve single and combined event probability problems without errors.
Mutually Exclusive Events Add Up to 1
All possible mutually exclusive outcomes must sum to exactly 1. If an event doesn't happen, use the complementary rule.
P(NOT Event) = 1 − P(Event). If P(Win) = 0.35, then P(Lose) = 1 − 0.35 = 0.65Independent Combined Events (AND Rule)
To find the probability of two independent events both happening (e.g. flipping heads AND rolling a 6), multiply their probabilities.
P(Heads and 6) = 1/2 × 1/6 = 1/12Expected Frequency (Number of Times)
To find how many times an event is expected to happen over multiple trials, multiply the probability by the total number of trials.
60 × 1/6 = 10 timesProbability Practice Worksheet
Download the accompanying question pack and full worked answer key.
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