Probability and Statistics
Core concepts
You must handle probability rules (addition, multiplication, conditional probability, independence), tree diagrams, discrete and continuous random variables, expectation and variance, the binomial and normal distributions, and basic descriptive statistics including mean, variance and standard deviation. Know when to use the binomial (fixed number of independent trials, constant probability) and when to use the normal (continuous, symmetric, specified mean and variance).
Traps
- Confusing P(A|B) with P(B|A); Bayes-type questions hinge on this distinction.
- For 'at least one' questions, use the complement: 1 − P(none).
- When approximating a binomial by a normal, use the continuity correction (e.g. P(X ≥ 5) becomes P(Y ≥ 4.5)).
- Use the sample variance divisor correctly; distinguish population and sample formulae when the question specifies.
- Mutually exclusive and independent are different: mutually exclusive events with positive probability are not independent.
Worked example
A fair coin is tossed 10 times. Find P(at least one head). P(none) = (½)^10 = 1/1024, so the answer is 1 − 1/1024 = 1023/1024 ≈ 0.999. Rule of thumb: 'at least one' almost always invites the complement.