Total probability — outcomes summing to 1
A foundational probability rule that recurs at every WJEC tier. Most often tested as "find the missing probability".
The rule
If outcomes are exhaustive (cover all possibilities) and mutually exclusive (none overlap), the probabilities sum to 1.
PA + PB + PC + ... = 1.
P(not A) = 1 − P(A)
Because A and "not A" together cover all outcomes:
PA + P(not A) = 1, so P(not A) = 1 − PA.
This is the complement rule.
Finding a missing probability — typical Foundation question
A spinner has four sectors: red, blue, green, yellow.
| Colour | Red | Blue | Green | Yellow |
|---|---|---|---|---|
| Probability | 0.3 | 0.2 | 0.4 | ? |
P(yellow) = 1 − 0.3 − 0.2 − 0.4 = 0.1.
Algebraic missing probabilities (Intermediate / Higher)
| Outcome | A | B | C |
|---|---|---|---|
| Probability | 2x | 3x | 0.4 |
2x + 3x + 0.4 = 1 5x = 0.6 x = 0.12.
So PA = 0.24, PB = 0.36.
Mutually exclusive vs not
Two events are mutually exclusive if they cannot both happen on the same trial. P(A or B) = PA + PB only when they are mutually exclusive.
(For overlapping events, see the addition law: P(A ∪ B) = PA + PB − P(A ∩ B), Higher only.)
WJEC exam tip
The mark scheme awards M1 for "all probabilities sum to 1" — write that explicitly as a line of working before subtracting. It guarantees the method mark even if the arithmetic stumbles.
AI-generated · claude-opus-4-7 · v3-wjec-maths-leaves