Example 1 · level 1 — a gentle start
A bag holds 5 red, 4 blue counters. One is taken at random. What is the probability it is red?
- 4/9
- 1/2
- 5/4
- 5/9
Answer: 5/9 — There are 9 counters altogether and 5 are red.
11+ probability questions
Probability comes up in the maths paper of every major 11+ format. Here is what the questions look like, the method that works under time pressure, and five worked examples with the full reasoning, from a gentle start to a hard paper.
Maths · examined by GL and CEM · 5 worked examples
What your child needs to know
- Probability is: how many you want, out of how many there are ALTOGETHER.
- 3 red counters in a bag of 8 gives a probability of 3/8.
Where marks get lost: The bottom number is the total — not the number of the other colours. That is the usual slip.
Worked examples
Every question below is generated by the same engine your child practises on, and every answer is derived by our checker rather than written by hand — which is why we can put them on a public page at all.
Example 2 · level 2 — typical of early practice
A bag holds 3 red, 8 blue counters. One is taken at random. What is the probability it is blue?
- 1/2
- 8/3
- 8/11
- 3/11
Answer: 8/11 — There are 11 counters altogether and 8 are blue.
Example 3 · level 3 — standard paper difficulty
A bag holds 12 red, 2 blue, 7 green counters. One is taken at random. What is the probability it is blue?
- 1/3
- 2/19
- 19/21
- 2/21
Answer: 2/21 — There are 21 counters altogether and 2 are blue.
Example 4 · level 4 — a harder paper
A bag holds 14 red, 16 blue, 9 green counters. One is taken at random. What is the probability it is blue?
- 16/39
- 16/23
- 1/3
- 23/39
Answer: 16/39 — There are 39 counters altogether and 16 are blue.
Example 5 · level 5 — the level that separates candidates
A bag holds 11 red, 2 blue, 19 green, 19 yellow counters. One is taken at random. What is the probability it is yellow?
- 32/51
- 19/51
- 1/4
- 19/32
Answer: 19/51 — There are 51 counters altogether and 19 are yellow.
How to practise this at home
- Work in short, frequent sessions. Ten minutes daily beats an hour at the weekend, because the recall gap is what builds memory.
- Insist on written working, even for questions your child can do in their head — under exam pressure the method is what survives.
- When an answer is wrong, ask them to explain their reasoning before you correct it. The error is almost always in one step, not the whole approach.
Practise probability with a tutor that explains
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