Playbook
Probability Distribution
115 q - 2.65/paper - 20% HARD. The highest-weight Quick-Win, worth over five marks a paper at a fifth the HARD rate of the calculus chapters. Classical Probability (21 q) runs 10% HARD; only Bayes and Conditional (26 q, 31%) has any real teeth.
- Questions in the bank
- 115
- q/paper (2024–25 shifts)
- 2.65
- Tagged HARD
- 20%
- Subtopics
- 4
Strand: Quick-Win
When you’ll see it
A random variable with a probability table, an expectation or variance to compute, a conditional statement, or a plain counting probability.
How this chapter is tested
115 q at 2.65 per paper and 20% HARD. This is the highest-weight Quick-Win in the subject and it is worth stating the trade plainly: over five marks a paper at roughly a fifth of the HARD rate of the calculus cornerstones. On a 90-minute paper with no negative marking, that is the best exchange of preparation time for marks available outside Applications of Derivative.
The difficulty is genuinely concentrated in one place. Classical Probability, Addition Theorem and Odds is 21 q at 10% HARD. Discrete Random Variables, PMF and CDF is 31 q at 19%, and Expectation, Variance and Standard Deviation is 37 q at 19% — the largest block and still under a fifth HARD. Only Conditional Probability, Independence and Bayes' Theorem (26 q, 31%) has any real teeth, and even that is below the subject average of 38.4%.
Almost every question in the first three subtopics runs the same pipeline: build or read a probability table, check it sums to 1, then apply a formula to it. That check is not busywork — a large share of the medium-difficulty questions in this chapter ARE the check, presented as finding an unknown constant in the table.
Two habits pay here. Write the distribution as an explicit table before doing anything, because it makes the sum-to-one check free. And when the options are numbers, remember that a probability outside the zero-to-one range is an immediate elimination, which at 1.8 minutes a question is a real lever.
The sub-skills
The distinct skills inside the chapter, in the order to learn them.
Classical probability, addition theorem, and odds
Favourable over total, the addition rule for unions, and converting between probability and odds. 21 q at 10% HARD — the cheapest block in the chapter and the place to start.
Discrete random variables, PMF and CDF
Read or construct a probability mass function, enforce that it sums to 1, and move between the mass function and the cumulative function. 31 q at 19% HARD.
Expectation, variance, and standard deviation
Expectation as the probability-weighted sum, variance as the mean of squares minus the square of the mean, and the standard deviation as its root. 37 q at 19% HARD — the largest block, and almost entirely mechanical once the table is written.
Conditional probability, independence, and Bayes' theorem
Conditioning restricts the sample space; independence means the conditioning changes nothing; Bayes reverses the direction of the conditioning. 26 q at 31% HARD, the only demanding block here.
Traps to expect
Distractor shapes this chapter reuses. The Traps page covers the patterns that cut across chapters.
Distribution that does not sum to one
A table with an unknown constant where the intended step is solving for it. Options computed from the unnormalised table are supplied, and they look entirely reasonable.
Conditional probability taken in the wrong direction
The probability of A given B and the probability of B given A are different numbers and both appear as options. This is the standard Bayes distractor.
Independent read as mutually exclusive
Two events cannot generally be both, and the two assumptions give different answers for the same stem. Read which one the question actually states.
Odds reported as a probability
Odds in favour of three to two is a probability of three fifths, not three halves, and odds against reverses it. Both wrong readings are offered.
Learn it before you drill it
This chapter has full teaching notes — foundations, worked examples, self-checks and a per-subtopic mastery checkpoint. Read the notes once, then drill subtopic by subtopic below.
Probability Distribution notesDrill every probability distribution question
115 questions from the bank, scoped to 4 bundled subtopics.
Drill one subtopic at a time
The 4 subtopics this playbook covers, in catalog order.
Related playbooks
Often paired with this one — the technique, the trap or the taxonomy overlaps. Drill these next.