All the probabilities add up to 1
For one trial, the probabilities of all possible outcomes sum to . Use this to find a missing probability: .
Expected frequency = P × trials
To estimate how many times an outcome happens in trials, multiply: .
Mutually exclusive "or": add
If two events cannot both happen, .
Drawn from real examiner reports.
Stopping at P when asked "how many"
Giving the probability (e.g. 0.24) and not multiplying by the number of trials to get the expected number.
Nov 2024 Paper 2H (Q5): students stopped at 0.24 rather than ×400.
Not subtracting the givens from 1
When two missing outcomes are equal, you must do first, then halve — not just halve the given total.
Nov 2024 Paper 2H (Q5): "192" came from not subtracting from 1 / not halving correctly.
Probabilities that add to more than 1
Combining events by adding when they overlap, producing a probability greater than 1.
Reported across Nov/June 2024 probability questions.
For "or", add — do not multiply
For mutually exclusive events P(A or B) = P(A) + P(B). Multiplying is for "and" (independent events happening together). Multiplying two "or" probabilities gives a value that is far too small.
A probability outside 0 to 1
Every probability must satisfy 0 ≤ P ≤ 1. An answer below 0 or above 1 is impossible — it usually means "or" events were added when they overlap, or an arithmetic slip crept in.
Complement is 1 − P(A), not P(A) − 1
P(not A) = 1 − P(A). Writing P(A) − 1 gives a negative number, which is impossible. Subtract the event probability from 1, not the other way round.
Use fractions/decimals, not ratios
A probability must be a number from to (fraction, decimal or percentage) — never a ratio like .
Check the outcomes sum to 1
Before finishing, add every outcome probability for one trial: they must total exactly 1. If they do not, a value is wrong or an outcome is missing.
Common denominator to add fractions
When adding fractional probabilities, rewrite them over a common denominator first. Adding numerators and denominators separately is a frequent slip that gives a wrong total.
A probability is a number from to . For one trial, all outcome probabilities add to : When two missing outcomes are equally likely, subtract the rest from first, then halve.
How do you find a missing probability for one trial?
A spinner can land on red, blue or green only. and . Find .
