Probability and Statistics: Reasoning Under Uncertainty
Core concepts
Candidates must handle basic probability rules (complement, addition, multiplication for independent events), conditional probability in simple settings, and the interpretation of summary statistics: mean, median, mode, range, and standard deviation as a measure of spread. You should also read and criticise data displays and recognise sampling bias.
Key relationships
P(not A) = 1 - P(A).P(A or B) = P(A) + P(B) - P(A and B).- For independent events,
P(A and B) = P(A) x P(B).
Traps to watch
- Adding probabilities of non-mutually-exclusive events without subtracting the overlap.
- Assuming independence from small samples or from events that are described as unrelated in everyday language.
- Confusing mean and median when data are skewed; the median resists outliers, the mean does not.
- Misreading a two-way table, particularly conditional probabilities where the denominator is a row or column total, not the grand total.
- Treating correlation as causation in interpretation questions.
Worked example
In a class of 30, 18 study French, 12 study Spanish, and 6 study both. The probability a randomly chosen student studies French or Spanish is (18 + 12 - 6)/30 = 24/30 = 0.8. The probability they study French given they study Spanish is 6/12 = 0.5 - note the denominator change, which is the single most common error.
Rule of thumb
Before computing, write the denominator explicitly. "Given that" always resets the denominator to the conditioning group.