Topic Brief: Conditional Probability Independence vs Mutually Exclusive

#SIGNAL Topic Master Brief — Conditional Probability, Independence vs. Mutually Exclusive (WST01, spec 3.2/3.3)

Provenance (2026-09-29): built entirely from research/veridian/WST01-verified-facts.md (compiled 2026-09-12, spot-check addendum 2026-09-25), grepped for "conditional", "independen" and "mutually exclusive". Cross-checked against signal-frequency-and-boundaries.md (this folder, whole- Section-3 count) and codex-deep-dive-conditional-probability-independence-vs-mutually-exclusive.md (this folder, formal proofs and micro-examples) so this document does not restate either — it narrows the frequency doc's Section-3-wide "4 of 6" figure down to this specific pairing and adds the mark-tariff/context-pattern layer neither existing document states as its own subject. No new PDF fetches were made. Every claim below cites a series and question from the facts bank.

#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 with a verified mark scheme: Jun 2019, Jan 2021, Oct 2021, Jun 2022, Jan 2023, Jun 2024. Within that set, this specific pairing — independence and mutual exclusivity treated as a calculation, not a judgment — is directly evidenced in 4 of those 6: Jan 2021, Oct 2021, Jun 2022, Jan 2023.

Jun 2019's spot-checked findings concern box plots and a discrete random variable (not this pairing), and Jun 2024's conditional-probability citations are all about the Normal distribution (spec 6.1, a different guidance box, taught in the sibling lesson on standardisation) — so neither of those two series adds a confirmed instance of 3.2/3.3 specifically. This is narrower than the "3.1–3.4 Probability, 4 of 6" row in signal-frequency-and-boundaries.md, which pools this topic together with tree/Venn sum-and-product-law questions (spec 3.4); the series list happens to be identical, but the two counts answer different questions and should not be read as the same claim doubly confirmed.

The other 8 series were not searched question-by-question for this topic. Their absence from the count is not evidence they lacked it — it is simply unread.

#2. What was actually tested, by series

• Jan 2021 Q1(c). Conditional probability compounded with a complement event, collapsed by candidates into a raw ratio of two marginals. ER quote: "we occasionally still saw P(0.35∩0.4)/0.4 or 0.35/0.4."
• Oct 2021 Q1(a)–(d), 7 marks per the facts bank. The richest single instance: a Venn diagram (events A, B, C, two unknowns) used to (a) find P(B) [M1, A1]; (b) determine whether A and B are independent by calculation rather than by eye [B1(ft), B1(ft), B1]; (c) use a given conditional- probability condition to solve a two-unknown system [M1, A1, A1]; (d) construct a new event mutually exclusive with A but overlapping B [B1]. Part (b)'s ER note: "there was the usual confusion between events being independent and events being mutually exclusive."
• Jun 2022 Q4(b), plus a paper-wide general comment that series. A Venn-diagram conditional- probability question where candidates wrongly assumed independence, and separately inverted a subtraction/division order. The general comment: "candidates often assume independence when an appropriate conditional probability should be used instead."
• Jan 2023 Q2(d). A later-stage conditional-probability calculation (not the independence/ME judgment itself) where an already-used probability was folded a second time into the numerator.

#3. Mark-tariff pattern

No fixed mark value repeats across series — this pairing is tested at different tariffs depending on how much of the surrounding question it anchors:

• As a standalone judgment (Oct 2021 Q1(b)): 3 marks, and structured as B marks, not M/A — the mark scheme's own convention for "an independent accuracy mark where there is no method." The independence-or-not conclusion itself is credited as a stated comparison, not a multi-step method.
• As the engine of a larger calculation (Oct 2021 Q1(c), Jan 2021 Q1(c), Jan 2023 Q2(d)): scored as ordinary M1/A1 method-and-accuracy pairs, where the error sits inside the fraction being built, not in a separate judgment step.
• Position in the paper is not fixed. This content opened the paper as Q1 in two of the four series (Jan 2021, Oct 2021), sat later as Q2(d) in Jan 2023, and later still as Q4(b) in Jun 2022. Do not coach students to expect it early.

#4. Recurring context/angle across the four series

Two distinct angles repeat, and they test different things:

1. A direct test, given numeric probabilities (Venn diagram in Oct 2021; implied two-way probabilities in Jun 2022) — the question explicitly asks whether two named events are independent or mutually exclusive, and the trap is answering by eye ("they overlap, so not independent") instead of running the one calculation that settles it.
2. A silent assumption inside an unrelated calculation (Jun 2022 Q4(b) and its general comment; Jan 2021 Q1(c)'s complement case) — the question never asks "are these independent?" at all; a candidate substitutes independence, or a plain marginal ratio, in place of the conditional- probability calculation the question actually requires.

Angle 2 is the more consistently damaging of the two: Pearson names it as a paper-wide diagnosis in the Jun 2022 report, not a slip confined to one question.

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

Expect it to arrive either as an explicit "determine whether A and B are independent" instruction attached to a Venn diagram or table with at least one unknown probability, or as a silent trap buried inside a conditional-probability calculation that never mentions independence by name. If it's the first kind, the mark is usually a standalone B-mark for the correct comparison and conclusion, not a multi-step method — get the one calculation right and state the conclusion explicitly. If it's the second kind, the risk is substituting independence, or a raw ratio of marginals, for the conditional- probability formula the question actually needs; check whether a P(X|Y) is required before reaching for P(X)×P(Y). A constructive variant — draw or describe a new event meeting stated overlap/mutual- exclusivity conditions — has appeared exactly once in the confirmed record (Oct 2021 Q1(d)); it is real but not yet established as a repeating pattern on this evidence.

#Sources and limitations

• All citations trace to research/veridian/WST01-verified-facts.md, §5 (Section 3) and the 2026-09-12 per-lesson audit of conditional-probability-independence-vs-mutually-exclusive.ts.
• Frequency is stated only as "N of 6 series checked" — no percentage or likelihood claim is made anywhere in this document, and no grade-boundary figure is used or implied (none exists in the source material; see signal-frequency-and-boundaries.md §2).
• The 8 series without a located examiner report (Jun 2021, Jan 2022, Oct 2022, Jun 2023, Oct 2023, Jan 2024, Oct 2024, Jan 2025) were not searched for this topic and are excluded from both the numerator and denominator above.
• This document does not repeat the formal proofs, micro-examples, or lesson-gap analysis already in codex-deep-dive-conditional-probability-independence-vs-mutually-exclusive.md, nor the whole- Section-3 frequency row in signal-frequency-and-boundaries.md.