Probability is the maths of chance. At 11+ level, it's straightforward — most questions involve fractions or simple yes/no logic. Here's the framework.
The 11+ probability scale
Every probability sits between 0 and 1:
- 0 = impossible (e.g. "rolling a 7 on a 6-sided die")
- 0.5 or ½ = even chance
- 1 = certain
The basic formula
Probability of an event = (number of favourable outcomes) ÷ (total possible outcomes).
Worked examples
Coin flip
What's the probability of flipping a head? Favourable: 1 (head). Total: 2 (head or tail). Answer: 1/2.
Dice roll
What's the probability of rolling an even number on a 6-sided die? Favourable: 3 (2, 4, 6). Total: 6. Answer: 3/6 = 1/2.
Bag of marbles
A bag has 3 red, 4 blue, 5 green marbles. What's the probability of pulling a red? Favourable: 3. Total: 12. Answer: 3/12 = 1/4.
Tricky question types
Without replacement
"A bag has 4 red and 6 blue marbles. You pull one (red) without putting it back. What's the probability the next is red?" After removing one red: 3 reds left, 9 total. Answer: 3/9 = 1/3.
Two events
"Probability of two independent events both happening" = multiply the two probabilities. Two coin heads: 1/2 × 1/2 = 1/4.
Common errors
- Forgetting "out of how many" — always check the total carefully.
- Reducing fractions before answering — examiners want fully simplified answers.
Quest Arena's maths worksheets include probability drills graded from foundation to advanced.