11+ Maths · Topic explained
Probability
Can you put a number on chance?
The big idea
Probability is a number from 0 to 1 that says how likely something is.
Picture it
Think of a line like a weather forecast: from impossible to certain.
Key words
- outcome
- One thing that could happen, like rolling a 4.
- impossible / certain
- Probability 0 means it can't happen; 1 means it must.
- even chance
- Just as likely to happen as not: 1/2.
- fair
- Every outcome is equally likely.
Worked examples
- 1Warm-up
A fair dice is rolled. P(rolling a 4) = ?
- 6 equally likely outcomes
- Only 1 of them is a 4
- P(4) = 1/6
- 211+ standard
A bag has 3 red, 5 blue and 2 green sweets. P(blue) = ?
- 3 + 5 + 2 = 10 sweets
- 5 of them are blue
- P(blue) = 5/10 = 1/2
- 311+ standard
The probability it rains today is 0.3. What is the probability it does not rain?
- It either rains or it doesn't: together they make 1
- 1 − 0.3 = 0.7
- 411+ standard
A bag has 20 counters. P(red) = 1/4. How many counters are red?
- 1/4 of the counters are red
- 20 ÷ 4 = 5 red counters
The common mistake
The mistake
Win or lose: two outcomes, so the chance is always 1/2.
Instead
It's only 1/2 if both outcomes are equally likely.
Why: 9 blue sweets and 1 red: picking red has two outcomes (red or not) but P(red) is only 1/10.
Where it comes up in the 11+
Bags of sweets, spinners and dice: give the answer as a fraction in its simplest form, a decimal or a percentage.
The video
Video coming soon
We're making a short video that explains probability step by step. Until then, everything it covers is on this page.
Free printable
Probability worksheet
Practice questions on this topic to print and try on paper, at home or on the way to school.
Download the worksheet (PDF)Free account needed: it takes a minute.
Quick quiz
Have a go first, then tap to see the answer.
1. A letter is picked at random from the word MATHS. What is the probability it is a vowel?
- 1/5
- 2/5
- 1/4
- 1/2
Show the answerHide the answer
1/5
Only A is a vowel: 1 letter out of 5.
2. Which of these has a probability of 0?
- Rolling an even number on a dice
- Rolling a 7 on a normal dice
- Tossing heads
- Picking a red card from a full pack
Show the answerHide the answer
Rolling a 7 on a normal dice
A normal dice only goes up to 6, so rolling a 7 is impossible.
3. A bag has 4 red balls and 6 yellow balls. What is P(yellow) as a decimal?
- 0.4
- 0.6
- 0.46
- 6
Show the answerHide the answer
0.6
6 yellow out of 10 balls: 6/10 = 0.6.