Video lecture (English) of C05 Probabilities
C05 Probabilities (I)
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
- Distinguish strictly between mutually exclusive and independent events to accurately calculate combined probabilities using the addition and multiplication rules.
- Exploit visual models by constructing and interpreting Venn and tree diagrams to evaluate conditional probabilities and sequential draws without replacement.
- Formulate algebraic probability equations from scenarios involving unknown quantities and solve the resulting linear or quadratic systems to find $n$.
- Apply complementary logic to bypass tedious multi-case calculations by efficiently utilising $1-\mathrm{P} (\text{None})$ the shortcut for “at least one” scenarios.
Suggested Time
| Task | No. of Questions | Suggested Time |
|---|---|---|
| Examples | 9 | 90 min |
| Quiz | 6 | 15 min |
| Practice A | 15 | 45 min |
| Practice B | 20 | 75 min |
| Total | 50 | approx. 3-4 hrs |
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