S1.1
Probability and Discrete Probability Distributions
Understand and apply probability; work with discrete random variables and their expected values.
Sample questions
- 1.A discrete random variable X has P(X = 0) = 0.3, P(X = 1) = 0.5, P(X = 2) = 0.2. Find E(X).
Exam weighting
3–5 marks.
Common student mistakes
- ·Confusing P(A ∪ B) and P(A ∩ B) in the addition formula
- ·Forgetting to check that probabilities sum to 1 in a distribution table
S2.1
The Binomial Distribution
Identify and apply the binomial distribution; calculate probabilities and expected values.
Sample questions
- 1.A fair coin is tossed 10 times. Find the probability of getting exactly 4 heads.
Exam weighting
3–5 marks.
Common student mistakes
- ·Not verifying the four conditions for a binomial distribution
- ·Using the wrong value of p (complementary event errors)
S3.1
Normal Distribution
Apply the properties of the normal distribution; use z-scores; model data with normal distributions.
Sample questions
- 1.Heights are normally distributed with mean 170 cm and SD 8 cm. Find P(158 < X < 186).
Exam weighting
3–5 marks.
Common student mistakes
- ·Incorrect z-score formula — dividing by σ² instead of σ
- ·Forgetting to account for both tails of a symmetric probability
Other Advanced topics
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