Technique Masterclasses

Statistics 1

Topic Brief: Elementary Probability and Conditional Notation

SIGNAL Topic Master Brief — Elementary Probability and Conditional-Probability Notation (WST01, spec 3.1/3.2)

Provenance (2026-09-29): built from research/veridian/WST01-verified-facts.md (compiled 2026-09-12, spot-check addendum 2026-09-25, Jan 2023 Q2(d) correction dated 2026-08-28), grepped for "Section 3", "3.1", "3.2" and the individual series citations quoted below, plus the per-lesson audit entry for elementary-probability-and-conditional-notation.ts (2026-09-12) for the real Jan 2021 Venn diagram's own values. Cross-checked against codex-deep-dive-elementary-probability-and-conditional- notation.md (this folder, §4's synthesis table) and signal-frequency-and-boundaries.md (this folder, whole-Section-3 count) so this document does not restate either. No new PDF fetches were made. This brief covers spec 3.1/3.2 notation literacy — sample-space counting, P(A′), the addition law, and conditional probability including compound-complement forms P(A∩B′)/P(A|B′) — which is a different slice from the sibling brief's spec 3.2/3.3 independence-vs-mutually-exclusive judgment ground; where the two overlap on the same series, this document says so rather than double-counting silently.

1. Frequency — seen in 4 of 6 series checked

The facts bank has a fully-read Principal Examiner Feedback report for 6 of the 14 WST01 series: Jun 2019, Jan 2021, Oct 2021, Jun 2022, Jan 2023, Jun 2024. This topic's own notation/counting error — as opposed to the independence-judgment error the sibling brief covers — is directly evidenced in 4 of those 6: Jan 2021, Oct 2021, Jun 2022, Jan 2023. It is not confirmed for Jun 2019 or Jun 2024; absence of a citation is not evidence of absence, only of an unread question. Two further series contribute a mark-scheme-only citation with no examiner-report error attached: Jan 2025 Q1(b) (classical probability, no documented error) and, more loosely, Oct 2022's mark scheme (an oe answer-form note, not this topic's error pattern specifically, so not counted in the "4 of 6").

Spec 3.1 alone — elementary probability with no conditional element — has no standalone examiner-report or mark-scheme question anywhere in the 14-series archive; it is tested embedded inside 3.2-level conditional-probability questions, never as its own separately-marked item. That is a confirmed absence, not an unchecked gap, and it means every citation below is really a 3.1+3.2 composite, not a pure 3.1 instance.

2. What was actually tested, by series

3. Mark-tariff pattern

No standalone mark value repeats, because this content never anchors its own whole question — it scores 1 mark as a single B-mark complement step (Jan 2021 Q1(a)), or 2 marks as an ordinary M1/A1(ft) pair one or two calculation-steps deep inside a larger tree- or Venn-diagram question (Jan 2021 Q1(b)– (c); Jan 2023 Q2(d)). Position in the paper is not fixed either: it opened the paper as Q1 in Jan 2021, but sat mid-paper as Q4 in both Oct 2021 and Jun 2022, and as Q2 in Jan 2023.

4. Recurring context/angle across the four series

Two distinct numerator-construction failures repeat, both variants of the same underlying mechanism — miscounting exactly which terms belong in a conditional probability's numerator once the sample space has been restricted:

  1. A dropped term. Oct 2021's tree diagram needed three branch-probability products summed into the numerator; the common answer used only two.
  2. A spurious extra term. Jan 2023's tree diagram needed the single clean path product as the numerator; the common answers re-added or re-multiplied the already-used denominator value back into it.

Jun 2022's "1 − 1/15 before dividing by 3/8" is a third, distinct flavour — an operator-ordering slip on a Venn diagram rather than a tree diagram — and Jan 2021's raw-ratio error (0.35/0.4 for a compound complement) is a fourth: substituting two marginals' plain ratio for the properly-restricted intersection-over-conditioning-event ratio. All four sit inside a conditional-probability calculation that also demands correct upstream notation (a complement, a union, a compound complement) before the conditioning step is even reached — this is why the topic is inseparable from spec 3.1's counting foundation in every real instance found.

5. If this topic appears, here's what to expect

Expect either an early, compound-notation question on a Venn diagram — a complement of a multi-region event, then the addition law, then a conditional probability whose conditioning event is itself a complement (Jan 2021's shape) — worth 1–2 marks per sub-part and penalising an unsimplified final fraction; or a mid-paper tree-diagram conditional probability where the real risk sits in the numerator's term count, not the formula itself: count exactly how many branch products the numerator needs before writing it down, and check nothing already used in the denominator has been folded back in. On this evidence, spec 3.1 by itself never carries its own question — treat it as the counting skill a 3.2 question always sits on top of, not as content to revise in isolation.

Sources and limitations