Probability
Use experimental and theoretical probability, systematic enumeration, trees, Venn diagrams and conditional reasoning.
How to prepare for the current TMUA
Secure the shared mathematical specification, practise application in unfamiliar settings, then make every Paper 2 implication and proof step explicit.
Core concepts
Concept 1
Connect relative frequency, theoretical probability and expected outcomes.
Exam cue: Ask whether the listed outcomes are exhaustive and equally likely.
Concept 2
Construct exhaustive possibility spaces and representations for combined events.
Exam cue: Check whether a previous outcome changes the next probability.
Concept 3
Distinguish mutually exclusive, independent, dependent and conditional structures.
Exam cue: Translate the condition into a restricted denominator or branch.
Risk pitfalls and guardrails
Adding probabilities along a sequential route.
Guardrail: Do not treat examples as proof, reverse an implication, cancel a possible zero or rely on calculator-only intuition.
Treating mutually exclusive events as independent.
Guardrail: Do not treat examples as proof, reverse an implication, cancel a possible zero or rely on calculator-only intuition.
Using the original sample space after conditioning.
Guardrail: Do not treat examples as proof, reverse an implication, cancel a possible zero or rely on calculator-only intuition.
Memory anchors
Exhaustive total
Probabilities of all possible outcomes sum to one.
Along a route
Multiply branch probabilities.
Across alternatives
Add mutually exclusive route probabilities.
Independent
One event does not change the probability of the other.
Conditional
Restrict attention to outcomes satisfying the condition.
Expected frequency
Probability multiplied by the number of trials.
Checkpoint rule
Do the check-up only after you can summarize each concept in one sentence and identify one dangerous pitfall from memory.
Knowledge Check (after reading)
Short check-up to confirm understanding of this module.
Check-up Questions
Two fair coins are tossed. Given at least one head, what is the probability of two heads?
A bag has 3 red and 5 blue balls. Two are drawn without replacement. What is P(both red)?
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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