STEP preparation guide
STEP Probability and Statistics: How to Play Section C
Each STEP paper carries twelve questions, and just two of them, Section C, are probability and statistics. That makes it the section candidates most often write off in advance. Yet STEP's scoring rule is that everything you attempt is marked and only your six best answers count, with no interest in which section they came from, so those two questions are worth very different amounts to different candidates. This guide sets out the slot logic of Section C, what STEP probability questions actually look like, how far they sit from A level statistics, why counting and conditional probability keep carrying the section, and the criteria for deciding whether Section C belongs in your main attack.
10 sections2,222 words12 min read5 official sources
- Papers
- 111
- Questions
- 1532
- Free to try
- 2
Section C at a Glance
- Seats on the paper
- Two of the twelve questions (with eight pure and two mechanics), each marked out of 20
- How scoring works
- Everything you attempt is marked, your best six answers count out of 120, and no section is capped
- What it tests
- Derivation, not data handling: no calculators, and no formulae booklet since 2019
- Promotion test
- A pure base reliably worth four-plus questions, plus past papers you regularly get past halfway
- Grade 1 boundary, 2026
- 62/120 on STEP 2 and 56/120 on STEP 3, with each paper set its own boundaries
Rules and figures follow the OCR STEP specification, the official scoring and results pages, the OCR FAQs and the Explanation of Results for STEP 2026. Boundaries move every year, so read the 2026 numbers as context rather than as permanent thresholds.
In short
- Section C shares the mechanics slot logic exactly: two of twelve questions, everything attempted is marked, only your six best answers count and no section is compulsory, so it is two seats in a candidate pool, not a required module.
- STEP probability questions are derivation, not data handling: with calculators banned and no formulae booklet, they test model building and distribution work, and the second half of a question usually runs on pure mathematics.
- Counting and conditional probability are the foundation of Section C: within the probability toolbox at A level and Further Maths level they need the fewest prerequisites and offer the deepest reasoning chains, so they repay focused practice best.
- There is a clear promotion test: only make Section C a main line once your pure base reliably yields four-plus questions and past-paper trials show you regularly getting past halfway; otherwise treat it as a second string supplying one or two candidate questions.
- In the exam, use Section C as your designated substitute: read all twelve questions first, keep one reserve, remember that switching carries no sunk cost, and do not scatter attempts across more than six questions.
I
Part 1 of 3
Sections 01 to 04
01
Where Section C sits: the same slot logic as mechanics
Start with the official architecture. STEP 2 and STEP 3 each carry twelve questions: eight pure mathematics in Section A, two mechanics in Section B and two probability and statistics in Section C, every one of them marked out of 20.
Twelve questions per paper, 20 marks each
Everything attempted is marked; only your six best answers count, out of 120
Section A: pure8 questions
- Enough questions on its own to fill all six scoring seats
- A pure-only paper is entirely legitimate
Section B: mechanics2 questions
- Shares Section C's slot logic exactly
- Equally not a compulsory module
Section C: probability and statistics2 questions
- Two seats in a candidate pool of twelve
- No restriction on how many you attempt from any section
Tap a branch to unfold
The scoring rule underneath this article needs stating precisely, because it is widely misremembered: you are not asked to pick six questions and commit. Everything you attempt is marked, and your grade is built from the six questions you answered best. The calculation is completely indifferent to provenance: six pure answers, or five pure plus one probability, or four plus one plus one, all score identically if the marks are the same. For a sense of scale, grade 1 on STEP 2 in the 2026 series fell at 62 out of 120, a little over ten marks per question across six answers. Against that backdrop, the right question about Section C is never "do I need to learn statistics for STEP". It is "can these two seats supply me with an answer worth twelve or more marks".
02
Slot economics: why eight pure questions are not quite enough
The arithmetic first: Section A alone offers eight questions and only six count, so a pure-only plan is entirely legitimate, and plenty of candidates set out with exactly that intention. The hidden assumption is that at least six of those eight pure questions will actually be workable for you on the day. In practice one will land on your weakest topic, and another will simply refuse to open at the first part. If your workable pool is exactly six, a single collapsed question forces you into territory you never prepared, at full exam pressure.
Eight
Pure questions Section A puts on the table
Six
Answers that finally count towards your grade
Seven to eight
Candidate pool once one Section C type is reliable
Train one Section C question type to reliability, counting being the classic choice, and the effect is to widen your candidate pool from six to seven or eight, turning selection from forced acceptance into genuine choice. Hold the official caveat alongside this: you may attempt as many questions as you wish, but OCR is explicit that it is not advisable, and that candidates who attempt more than six rarely score as well as those who concentrate on six. So the point of widening the pool is not to answer more questions. It is to raise the quality of the six you finally submit. What you buy by practising Section C is not the marks of a seventh answer; it is the right to choose your best six.
03
What STEP probability questions actually look like: derivation, not data handling
Calculators
Neither permitted nor required
An exam that physically bans them cannot ask you to run a calculation procedure
Formulae booklet
Not issued; discontinued from 2019
Distributions and formulae have to be derived or remembered
Formats ruled out
Processing data sets, sample statistics, reading tables
Exactly the formats most familiar from A level statistics lessons
What remains
Build the model, derive distributions, compute expectations, prove results
Translate the wording into a probability model, then derive
OCR's description of STEP's question character applies with full force here: applying mathematical knowledge in novel and unfamiliar ways, often drawing on several specification topics, demanding insight, ingenuity, persistence and substantial sequences of algebraic manipulation. In Section C that plays out as questions which begin as probability and turn into pure mathematics halfway through. A sum over a distribution becomes a series manipulation; a continuous model becomes an integral; a bound becomes an inequality argument. Most STEP "statistics" questions are pure questions wearing probability clothing: the first half examines whether you can build the model, the second half whether your pure engine can carry it home.
04
How far Section C sits from A level statistics
| A level statistics | STEP Section C | |
|---|---|---|
| Core skill trained | Using: apply given formulae, run calculator procedures, follow standard methods on data | Constructing: define your own events, set up the model, derive distribution and expectation from first principles |
| Tools allowed | Leans heavily on the calculator and on given formulae | No calculator and no formulae booklet; most of the machinery comes from pure maths |
| Overlap between the two | Built around data handling and applying standard procedures | Examines almost none of that; the overlap is smaller than most students expect, and an A level statistics grade predicts very little here |
| How to prepare for Section C | Not by revising your A level statistics notes | By learning it as a new question type from scratch |
The converse also holds. A candidate who "dislikes statistics" but has a solid pure base and enjoys counting arguments can find Section C surprisingly profitable, because what the section actually consumes is pure technique and modelling precision. The marking works in your favour here too: OCR explicitly rewards good progress towards a solution, so a correctly built model and cleanly derived early parts earn real credit even if the final part escapes you, and a correct answer receives full marks whatever the method used.
II
Part 2 of 3
Sections 05 to 08
05
Counting and conditional probability: why they carry the section
The cleanest way to see this is from the syllabus level. STEP 2 is based on A Level Mathematics and AS Level Further Mathematics; STEP 3 on A Level Mathematics and A Level Further Mathematics. At that level the probability toolbox available to a question setter is genuinely small, and within it, counting and conditional probability are the two areas with the lowest prerequisites and the greatest reasoning depth.
Counting
Depends on almost no theory
Everyone has covered it, yet what is being counted, whether anything is double-counted or missed, and the whole structure are built by you, under strict case discipline
Conditional probability
Naturally layered
Information arrives in stages and the model must update in stages, the sharpest test of whether you turned a verbal scenario into a precise mathematical object
Fit with STEP's question character
Near-perfect
Novel contexts, cross-topic reach, insight and persistence all line up, which makes their recurrence in Section C structural rather than coincidental
What to do about it
Build the foundation here
Practise these two to depth rather than spreading effort evenly across every probability topic
06
Section C on STEP 2 versus STEP 3
The two papers differ first in their syllabus bases, and only after that in perceived difficulty.
| STEP 2 | STEP 3 | |
|---|---|---|
| Syllabus basis | A Level Mathematics + AS Level Further Mathematics | A Level Mathematics + A Level Further Mathematics (the specification notes the Further Maths pure content carries some removals and additions) |
| Grade 1 boundary, 2026 | 62/120 | 56/120 |
| Reached grade 1 or above, 2026 | 28.14% | 35.73% |
| What to expect in Section C | Stays closer to single-maths probability reasoning | Draws more freely on Further Maths level pure machinery, with heavier series work, integration and algebra, and more demand on continuous models and general proofs |
Both papers share the same derivation-first character.
Read the numbers carefully. STEP 3's lower grade 1 boundary and higher pass proportion should not be read as "Section C is easier on STEP 3". OCR explains that boundaries are set so that the offers met closely match the places available at the official user institutions (Cambridge, Warwick and Imperial College London), and therefore move with each year's cohort; each paper is set its own boundaries, so comparing boundaries across papers is not a measure of difficulty. Treat the 2026 figures as context, not as permanent thresholds.
07
Should Section C join your main attack? A decision framework
Do not decide by taste. Walk through four questions.
01Question 1
How many papers are you sitting?
Cambridge Mathematics applicants are normally asked to take both papers, which means four Section C questions across the season, so one well-trained question type serves two exams. Warwick accepts either paper, halving the seats, so the return on investment shrinks accordingly.
02Question 2
Is your pure base secure?
Promote Section C only once you can reliably land four or more pure questions. The logic is direct: the second half of a Section C question is pure mathematics anyway, so an unstable pure base caps whatever probability skill you build on top of it.
03Question 3
Run the empirical test
Pull the Section C questions out of several recent past papers, attempt them, and record how often you get past the halfway point. That percentage is worth more than any feeling: a high rate means this question type suits you and deserves more investment.
04Question 4
Weigh the marginal cost
If you already enjoy counting puzzles and probability riddles, reaching reliability is cheap. If you would be rebuilding probabilistic intuition from zero, the same hours pointed at your weakest pure topics usually pay better.
For most candidates the conclusion is to position Section C as a second string: a dependable source of one or two candidate questions and insurance against a pure collapse, not a pillar co-equal with pure. The eight pure questions remain the first priority, always.
08
Section C decisions in the exam room
At the start, read all twelve questions, including both Section C questions, even if your plan is pure-first. Do not skip them out of section prejudice. The scoring rule means switching carries no sunk cost: everything you attempt is marked and only your six best answers count, so an abandoned attempt cannot drag your grade down; it only costs the time you spent on it.
The practical routine: after the read-through, choose six questions to attack and designate one substitute. Section C often makes a good substitute because the opening part of a counting question tends to have a friendly entry point, letting you convert quickly after a switch. When a main-line question jams, switch decisively rather than fighting it.
Does STEP issue scratch paper?
No. Rough work goes in the answer booklet itself, and you simply cross out what you do not want.
Is crossed-out work marked?
Not unless you clearly indicate that it should be.
What has to go on each page?
Every page you write on must be labelled with the question number, as the booklet instructs.
Can I scatter attempts across seven or eight questions?
Resist it. OCR is explicit that candidates who do so rarely score as well; the right use of three hours is to finish six questions properly.
III
Part 3 of 3
Sections 09 to 10
09
Where marks leak: presentation and rigour
The official requirement is blunt: solutions must be clear, logical and legible, with working fully set out, and marks may be lost if examiners cannot follow your working, even when the final answer is correct. Probability is where this rule bites hardest, because probabilistic language is naturally slippery: undefined events, an unstated meaning of "at random", a case analysis with a missing branch. Habits that survive A level marking will sever the credit chain entirely in STEP.
Rule 1
Define first, argue second
Set out your events and random variables in notation before you argue, then argue in that notation throughout
Rule 2
State your assumptions
Independence and equal likelihood are premises to be written down, not defaults to be assumed silently
Rule 3
Make counting auditable
Say what is being counted and how you know nothing is double-counted or missed
Two rules work in your favour meanwhile: progress towards a full solution earns marks, so set the model up in full and secure the early parts; and any correct method earns full marks, so an elegant counting argument and a laborious complete enumeration are worth the same, and you should take whichever route you can write most clearly. In STEP, clarity is itself worth marks.
10
A training path built on official resources
Build your training on the official free resources first. The STEP Support Programme, developed by the Cambridge Faculty of Mathematics, is free and open to everyone, with online modules, hints and full solutions. Cambridge has also written fully worked solutions for STEP 2 and STEP 3 papers from 2019 onwards, and recommends using them to assess progress on timed papers once the STEP 3 modules are done.
01Stage 1
Start with the official modules
Work through the STEP Support Programme's online modules, hints and full solutions. It comes from the Cambridge Faculty of Mathematics and is free and open to everyone.
02Stage 2
Work Section C in themed passes
Extract the probability and statistics questions from recent past papers and work them in blocks by type: counting, conditional probability, discrete distributions, continuous distributions. Blocked practice builds pattern recognition faster than chronological grinding, and it exposes quickly where your genuine advantage lies, which is exactly the data the decision framework above asks for.
03Stage 3
Full timed papers, decisions included
Finish with full timed papers, and treat the decision process itself, the read-through, the selection, the substitution, as part of what you are training. Force yourself to execute the full twelve-question scan and name a substitute in every mock. In STEP, choosing questions well is worth as much as solving them well, and that skill only develops under full-paper timed conditions.
One caution when digging through archives: STEP 1 has not been offered since the June 2021 sitting, so when you run into old STEP 1 papers, do not treat them as samples of the current examination.
FAQ
Frequently asked questions
Can I skip the probability and statistics questions in STEP entirely?
Yes. There is no restriction on how many questions you attempt from any section, only your six best answers count, and Section A offers eight pure questions, enough to fill every scoring seat. But understand the leverage: your candidate pool shrinks to eight, and if any two pure questions go wrong on the day you have no fallback. Even candidates who are firmly pure-first usually train at least one Section C question type, typically counting, to a usable standard.
How different is STEP probability and statistics from A level statistics?
The difference is fundamental. A level statistics is built around data handling and applying standard procedures, leaning heavily on the calculator. STEP permits no calculator and issues no formulae booklet, and Section C examines derivation from first principles: build the model yourself, derive distributions, compute expectations, prove results, with most of the machinery coming from pure maths. An A level statistics grade therefore predicts little about STEP Section C, and the two should be trained as separate skills.
Why do counting and conditional probability matter so much for STEP Section C?
It follows from the syllabus level. STEP 2 is based on A Level Maths plus AS Further Maths, STEP 3 on A Level Maths plus A Level Further Maths, and within the probability toolbox available at that level, counting and conditional probability need the fewest prerequisites while offering the deepest reasoning chains. That makes them the natural carriers of STEP's question character, novel contexts and long chains of reasoning, and hence the structural core of Section C. Practising them to depth pays better than spreading effort across every probability topic.
How does Section C compare between STEP 2 and STEP 3?
STEP 2 is based on A Level Maths plus AS Further Maths, while STEP 3 rests on A Level Maths plus A Level Further Maths, with the specification noting some removals and additions to the pure content. STEP 3's Section C accordingly draws more freely on Further Maths level machinery such as series and integration, and asks more of continuous models and general proofs. In 2026 the grade 1 boundary on STEP 3 (56/120) was lower than on STEP 2 (62/120) while more candidates reached grade 1 (35.73% against 28.14%), but boundaries are set for each paper separately, by reference to the places available at the user institutions and the cohort's performance that year, so these figures do not mean STEP 3 is easier.
When should I attempt the probability questions during the exam?
Read both Section C questions during your opening scan of all twelve, and mark the one with the friendlier entry point. Because everything attempted is marked and only your six best count, switching has no sunk cost, so Section C works best as your designated substitute when a main-line question fails. If a Section C question is already among your chosen six, simply order it by confidence like the rest. The one thing to avoid is scattering attempts across more than six questions; OCR is explicit that such candidates rarely score as well.
Do I get marks for an unfinished probability question?
Yes. The marking explicitly rewards good progress towards a full solution: a correctly defined model and cleanly derived early parts earn real credit, and a correct answer receives full marks whatever the method. The condition is that your working must be followable: define events and random variables first and state your assumptions, because steps the examiner cannot follow can lose marks even when the idea is right.
What should I use to practise STEP Section C?
Start with the official free resources: the STEP Support Programme from the Cambridge Faculty of Mathematics, with online modules, hints and full solutions open to everyone, plus the officially written worked solutions for STEP 2 and 3 papers from 2019 onwards. In the focused phase, group past Section C questions by type and work them in blocks, then return to full timed papers. When using older archives, remember STEP 1 has not been offered since the June 2021 sitting, so do not treat STEP 1 papers as a template for the current exam.
MORE GUIDES
Other STEP preparation guides
- Your STEP revision plan: from first module to results day
- The STEP Support Programme: How to Use It, and What It Leaves Out
- STEP 2: Format, Marking, Grade Boundaries and Preparation
- STEP 3: What It Tests, How Hard It Is, and How to Prepare
- STEP Section A pure mathematics: the eight questions that decide your grade
- STEP Mechanics: The Strategic Case for Section B
- Writing STEP Solutions: Turning Maths You Can Do into Marks You Get
- STEP question selection: finding your best six out of twelve
- STEP grades and grade boundaries: from raw marks to offer conditions
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