Statistics and Probability

Outfit counting = trousers × shirts. Calculate each person’s total, then subtract to find the difference.

Multiplication counting principle questions appear in the very easy band of Selective MR. They’re quick marks when you multiply correctly, but students who add instead of multiply will get a wrong total and compare incorrectly.

The examiner checks whether students (1) multiply (not add) trousers × shirts for each person and (2) correctly compare 12 and 10 to determine who has more and by how much.

Two people have different numbers of clothing items. Students calculate the number of outfit combinations for each and compare them.

Bag-of-marbles probability always starts the same way: write each colour as a fraction over the total, then check every statement on its own before you pick an answer.

Three-statement probability items appear throughout Selective MR — students who convert to fractions immediately avoid the intuition traps on “equally likely” claims.

The examiner checks whether you compare probabilities with the same denominator, spot false equalities, and do not confuse “greater than” with “equal to”.

A bag lists counts for several colours. Three claims compare probabilities (greater than, equal to, etc.). You identify which claims are true.

A frequency table shows how many people own 0, 1, 2, 3 or 4 pets. To find total pets, multiply each pet count by how many people own that many — then add those products. Don’t just add the two columns separately.

Weighted frequency table questions (find the total quantity, not just the count of respondents) appear in the easy-to-medium band of Selective MR. The most common trap is adding the 'number of people' column and presenting that as the answer.

The examiner checks whether students multiply each value by its frequency (0×7, 1×12, 2×6, 3×9, 4×5) and sum the results, rather than summing the frequency column (39 people) or the value column (0+1+2+3+4=10).

A two-column table lists values (e.g. number of pets) and their frequencies (number of people). Students find the total of the measured quantity across all respondents.

Blue = twice yellow, red = blue. Pick a small number for yellow, work out the rest, then read off the probability as a fraction of the total.

Ratio-based probability questions (express counts as a ratio, then convert to probability) appear in the medium band of Selective MR. Students who jump straight to 1/3 or 1/2 without carefully reading each ratio clue will get it wrong.

The examiner tests whether students (1) correctly translate ‘twice as many blue as yellow’ (blue = 2 × yellow, not yellow = 2 × blue), (2) add all three colours to find the total, and (3) express the blue count over the total as a simplified fraction.

A container holds objects of three colours. The counts are related by ratios. Students find the probability of selecting one specific colour.

Total = 36, blue = 16, P(red) = 1/2. Red = 1/2 × 36 = 18. Yellow = 36 − 16 − 18 = 2.

Probability-to-count problems (use a given probability to find a count, then subtract to find a third colour) appear in the easy band of Selective MR. Students who forget to subtract both known colours will pick 20 (36−16) or 18 instead of 2.

The examiner tests whether students (1) multiply probability by total to find red count, (2) then subtract both blue AND red from 36 to get yellow, and (3) do not confuse 18 (red count) with the yellow answer.

A bag has three types of objects. One count and one probability are given. Students find the third count.

P(blue) = 0.2. Red = 2 × blue, so P(red) = 0.4. P(green) = 0.3. All four colours must sum to 1: P(yellow) = 1 − 0.2 − 0.4 − 0.3 = 0.1.

Four-colour probability questions with a ratio constraint appear regularly in Selective MR. The key step students miss is translating ‘twice as many red as blue’ into P(red) = 2 × P(blue), not P(red) = P(blue) + 2.

The examiner checks whether students (1) correctly convert the ratio clue into a probability, (2) sum all four probabilities to 1, and (3) subtract three known values to find the fourth.

A bag contains several colours. Probabilities of two colours are given directly; a third is defined as a multiple of another. Students find the fourth probability using the total = 1 rule.

When a question bundles average, median, and “above average” claims together, compute the average and median first — then test each statement with arithmetic, not guesswork.

Multi-claim statistics questions appear in the medium band of Selective MR — reliable marks when you sort the data and use mean = sum ÷ count.

The examiner tests whether you can find the mean and median from a small data set and judge comparative claims (e.g. how far above the mean a score is).

Five or six scores are given in a table. Three claims mention the average, a comparison to the average, and the median. You decide which claims are correct.

Jonas has CHEESE (6 cards) and Keeva has BEES (4 cards). Before you check any statement, count exactly how many of each letter each person has — repeated letters count every time.

Two-person multi-statement probability comparisons appear regularly in Selective MR. The examiner exploits three traps: (1) using 1/4 instead of 1/6 for C in CHEESE, (2) not noticing S appears once in both decks but the decks are different sizes, (3) assuming 3 Es vs 2 Es means Jonas is 'more likely' without comparing the fractions.

The examiner tests whether students (1) count repeated letters correctly in each word, (2) compute probabilities as exact fractions (not just counts), and (3) compare fractions across different denominators before declaring a statement true or false.

Two people each have a set of letter cards made from a given word (repeated letters appear on separate cards). Each picks one card at random. Three statements compare their probabilities. Students identify which are correct.