Wanted on top, altogether underneath: probability
The Short Answer
A probability is the number of outcomes you want over the number altogether, cancelled down. What the 11+ adds is that the total is often not given — it has to be worked out from a table or a sentence — and that removing an item changes both the top and the bottom, which is where most marks on this topic go.
What is a probability question?
How likely something is, written as a fraction: the number you want on top, the number altogether underneath, cancelled down.
Your child has been able to do that since Year 4. What the transfer test does is stop making it easy in three specific ways.
It stops drawing you the bag
The total is frequently not printed. Your child gets a table of colours, or a sentence describing the contents, and has to assemble the total before a fraction can be written at all.
That makes working out the total the first step rather than something that happens along the way — and getting it wrong makes everything after it wrong.
It wants the fraction cancelled
Four red counters out of ten is 4/10, which should be given as 2/5.
Marks go on this more often than they should, because the working is right and the presentation is not.
It takes a counter out halfway through
This is where most of the marks on the topic go.
Comparing two chances
Which is more likely, 2/5 or 3/8?
You cannot tell by looking, and the question is set that way on purpose. Put them over the same bottom number, exactly as with any two fractions: 16/40 against 15/40.
So 2/5 is the larger — by a whisker, which is why it had to be calculated.
The five words
Along the line from nought to one: impossible, unlikely, even chance, likely, certain.
Even chance means one half. It does not mean there are two possibilities. A bag with one red counter and nine blue has exactly two possible outcomes and a one-in-ten chance of red — so the number of possibilities tells you nothing about how likely each is.
Where do pupils lose marks?
Leaving the fraction uncancelled.
Changing the top and not the bottom after something is removed.
Assembling the total wrongly when it was not printed.
Reading 'even chance' as 'two options'.
Try it yourself
Work out the total first — it is often not given. Cancel your fraction before answering.
- A bag holds 4 red and 6 blue counters. What is the probability of drawing a red?
- Which is more likely: a chance of 2/5 or a chance of 3/8?
- A bag holds 6 red and 4 blue. One red is taken out and not replaced. What is the chance the next is red?
- What does 'even chance' mean?
- Why is working out the total the first step rather than the last?
- 2/5. Four wanted out of ten altogether, cancelled down from 4/10.
- 2/5. Put them over a common bottom: 2/5 is 16/40 and 3/8 is 15/40, so 2/5 is larger. You cannot tell by looking, which is exactly why the question is asked that way.
- 5/9. Both numbers change — five reds remain, and nine counters altogether. Children who only change the top get 5/10, which is a plausible and wrong answer.
- One half. Not 'there are two possibilities' — a bag with one red and nine blue has two possible outcomes and nothing like an even chance.
- Because the paper frequently does not print it. You may be given a table of colours, or a sentence describing the contents, and the total has to be assembled before any fraction can be written. Getting it wrong makes every subsequent step wrong too.
How much practice does this type need at home?
A pack of cards or a bag of mixed sweets, and one question repeated: what is the chance of drawing a red one?
Then eat one and ask again. The second question is the whole topic, and doing it with real objects — where your child can see the bag getting smaller — teaches the changing denominator far better than any explanation.
Free: a Maths workbook
Questions across the Maths question types, with the method printed at the top and full answers at the back. One workbook for the whole strand, not a sheet per question type.
Frequently Asked Questions
How do you compare two probabilities that are not obviously different?
Put them over the same bottom number, exactly as you would to compare any two fractions. 2/5 and 3/8 both go over 40 — sixteen fortieths against fifteen fortieths — so 2/5 is larger. There is no way to see that by looking at the original fractions, and questions are set precisely so that there is not.
What happens when a counter is taken out?
Both numbers change, and this is where most of the marks on this topic go. Take a red from a bag of 6 red and 4 blue and there are 5 reds left out of 9 counters — so the chance of another red is 5/9. Children reliably change the top and forget the bottom, giving 5/10. Ask them out loud: how many are in the bag now?
Does 'even chance' just mean there are two options?
No, and it is worth correcting early. Even chance means one half — the two outcomes are equally likely. A bag with one red counter and nine blue has exactly two possible outcomes and the chance of red is one tenth. The number of possibilities says nothing about the likelihood of each.
How should a probability be written?
As a cancelled fraction, unless the question asks for something else. 4/10 should be given as 2/5. Some questions want a decimal or a percentage, and some want a word from the scale — impossible, unlikely, even chance, likely, certain — so it is worth glancing back at the question before writing, since the work is identical and the form is not.
Sources
- GL Assessment — 11+ familiarisation materials and question type descriptions Published 2025.
- Clever Clogs Academy — our own Year 4 and Year 5 lesson records, Winslow Published September 2025 to July 2026.
We are not affiliated with, endorsed by or connected to GL Assessment or Buckinghamshire Council. Test arrangements change; always check the council's own pages for the current year's dates.
We Teach This Method Every Week in Winslow
Groups of no more than six pupils with two qualified teachers, in person or online. Come and see a session before you decide.