Interactive Coursebook (Online) of C09 Probabilities
C09 Probabilities (II)
What’s on the Specification
| M7.1 | Analyse the frequency of outcomes of probability experiments using tables and frequency trees. |
| M7.2 | Apply ideas of randomness, fairness and equally likely events to calculate expected outcomes of multiple future experiments. Understand that if an experiment is repeated, the outcome may be different. |
| M7.3 | Relate relative expected frequencies to theoretical probability, using appropriate language and the ‘0 to 1’ probability scale. |
| M7.4 | Apply the property that the probabilities of an exhaustive set of outcomes sum to one. Apply the property that the probabilities of an exhaustive set of mutually exclusive events sum to one. |
| M7.5 | Enumerate sets and combinations of sets systematically, using tables, grids, Venn diagrams and tree diagrams. Candidates are not expected to know formal set theory notation. |
| M7.6 | Construct theoretical possibility spaces for single and combined experiments with equally likely outcomes, and use these to calculate theoretical probabilities. |
| M7.7 | Know when to add or multiply two probabilities, and understand conditional probability. Calculate and interpret conditional probabilities through representation using expected frequencies with two‑way tables, tree diagrams and Venn diagrams. Understand the use of tree diagrams to represent outcomes of combined events:
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Learning Objectives
- Apply combinatorial counting methods—including combinations, permutations, and factorial logic—to accurately calculate the size of complex sample spaces and specific event outcomes under strict constraints.
- Evaluate infinite-state games of chance by mapping repeating or alternating turns to convergent geometric series to calculate the absolute probability of a player winning.
- Synthesise cross-domain concepts to solve complex scenarios where probability models interact directly with other mathematical fields, such as geometric intersections, vectors, or polynomial roots.
- Deconstruct conditional combinatorics to evaluate complex Bayesian probabilities, accurately adjusting calculations when the overall sample space is drastically restricted by a known post-event condition.
Suggested Time
| Task | No. of Questions | Suggested Time |
|---|---|---|
| Examples | 14 | 120 min |
| Quiz | 7 | 20 min |
| Practice A | 30 | 75 min |
| Practice B | 20 | 75 min |
| Total | 71 | approx. 4-5 hrs |
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