Maths

Probability (Higher)

Edexcel 1MA1 P

GCSE Maths (1MA1) · Higher · exam-style practice, examiner-report intelligence and the tools that drill it.

Verified against Edexcel 1MA1 (2026 spec)

The topic on one screen

  • The probabilities of an exhaustive set of outcomes sum to 1 — the fastest route to a missing probability.
  • Tree diagrams: multiply ALONG the branches, add BETWEEN the separate paths that satisfy the event.
  • 'Without replacement' changes the second fraction's numerator AND denominator — the classic dependent-probability trap.
  • Conditional probability P(A given B)=P(A and B)P(B)P(A \text{ given } B) = \dfrac{P(A \text{ and } B)}{P(B)}: restrict yourself to the BB world, then count.
  • Venn diagrams: fill the intersection first, then work outwards so nobody is double-counted.
  • 'At least one' is almost always fastest as 1−P(none)1 - P(\text{none}).

Where students actually lose marks

On 'without replacement' trees the second-branch denominator must drop by one; leaving it unchanged is the single most common lost mark on the topic.

Edexcel 1MA1 Higher — recurring tree-diagram error

A probability must be written as a fraction, decimal or percentage — giving a ratio or '3 out of 10' where a probability is asked can lose the mark.

Edexcel 1MA1 mark-scheme conventions (form of a probability)

Conditional questions are marked on dividing by the CONDITIONING event, not the overall total — dividing by the grand total is the standard error.

Edexcel 1MA1 Higher — recurring conditional-probability error

Try it — exam-style

Medium
3 marks
ORIGINAL

A biased spinner lands on red, blue or green. P(red)=0.4P(\text{red}) = 0.4, and P(blue)P(\text{blue}) is twice P(green)P(\text{green}). Work out P(green)P(\text{green}).

Medium
2 marks
ORIGINAL

A bag holds 5 red counters and 3 blue counters. Two counters are taken at random without replacement. Work out the probability that both are red.

Medium
2 marks
ORIGINAL

Using the same bag of 5 red and 3 blue counters, two taken without replacement, work out the probability of getting at least one blue counter.

Hard
2 marks
ORIGINAL

In a group of 30 students, 18 study French, 12 study German and 7 study both. A student who studies French is chosen at random. Work out the probability that they also study German.

Medium
2 marks
ORIGINAL

A box has 4 green and 6 yellow sweets. Two are eaten at random without replacement. Given that the first sweet was green, work out the probability that the second is yellow.

Medium
3 marks
ORIGINAL

Events AA and BB are independent with P(A)=0.3P(A) = 0.3 and P(B)=0.6P(B) = 0.6. Work out P(A and B)P(A \text{ and } B) and P(A or B)P(A \text{ or } B).

Questions are written in the style of past Edexcel papers (source shown on each) — never copied from them.

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Drill it properly

Mental Maths Trainer

Fast fraction arithmetic — the speed tree diagrams assume.

Formulae to Memorise

The addition and multiplication rules, and when each applies.

GCSE maths flashcards

Independent vs dependent, and the conditional-probability routine.

Stuck on probability (higher)?

Probability marks are lost on the setup, not the arithmetic — I teach the tree-and-Venn discipline that makes them routine, and your first lesson is free.

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