Probability at this level is counting, not theory. How many ways can the thing happen, over how many things could happen at all.
Children overthink it because the word sounds advanced. The maths is a fraction.
Maths carries 25% of the marks. Almost all of it arrives as worded problems rather than bare calculations, so the reading is part of the maths.
One rule, and that is all
Probability = the number of ways it can happen, divided by the total number of possible outcomes.
Write it as a fraction. Simplify if asked. That is the whole method.
The scale from 0 to 1
| Value | Means | Example |
|---|---|---|
| 0 | Impossible | Rolling a 7 on an ordinary dice |
| 1/2 | Even chance | A fair coin landing heads |
| 1 | Certain | Rolling a number less than 7 |
A probability can never be less than 0 or more than 1. If a child produces an answer outside that range, something has gone wrong, and that check alone catches a lot of errors.
Worked examples
A bag holds 3 red counters and 5 blue. What is the probability of drawing red?
- Ways it can happen: 3
- Total outcomes: 3 plus 5, which is 8
- Probability: 3/8
The error here is answering 3/5, using the other colour as the denominator instead of the total. The bottom number is everything in the bag.
What is the probability of rolling an even number on a standard dice?
Even numbers are 2, 4 and 6, so 3 ways out of 6 outcomes: 3/6, which simplifies to 1/2.
The two traps
- The denominator is the total, not the number of the other thing. In a bag of 3 red and 5 blue, the bottom is 8.
- "Not" questions. The probability of not red is 1 minus the probability of red. With 3/8 red, not red is 5/8. Children recalculate from scratch and often slip; "one minus" is quicker and safer.
Beyond those two, this is one of the most reliable topics in the paper. It rewards care rather than cleverness, which makes it worth banking.
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The word sounds harder than the maths
Children hear probability and expect something difficult, and then overthink a question that is a fraction. How many ways can it happen, over how many things could happen. That is it at this level.
The one thing worth drilling is the denominator. Three red and five blue, and a surprising number of children write three over five. The bottom number is everything in the bag, always.
After that it is one of the safest topics in the paper. I would make sure a child has it secure precisely because it is winnable, and then spend the time saved on worded problems, which is where the marks are genuinely hard to get.
Mushtaque Ahmed, Founder of GrammarPath and Bright Mentors
Frequently asked questions
How do you work out probability in the 11+?
Count the ways the thing can happen and divide by the total number of possible outcomes. A bag with 3 red and 5 blue counters gives a probability of 3/8 for red, because the denominator is everything in the bag.
What is the commonest probability mistake?
Using the other quantity as the denominator instead of the total. With 3 red and 5 blue, children write 3/5 rather than 3/8. The bottom number is always everything that could happen.
How do you answer a 'not' probability question?
Subtract from 1. If the probability of red is 3/8 then the probability of not red is 5/8. Recalculating from scratch works but invites slips, whereas one minus is quick and safe.
What does a probability of 0 or 1 mean?
Zero means impossible and one means certain. A probability can never fall outside that range, so an answer below 0 or above 1 signals an error, which makes it a useful quick check.
Is probability a hard 11+ topic?
No, it is one of the most reliable in the paper once the single rule is understood. It rewards care rather than cleverness, so it is worth banking the marks rather than worrying about it.