135 questions · 21 question types identified
Select a committee or group of a fixed size from a larger population with no restrictions or simple restrictions like 'must include person X' or 'cannot include both X and Y together'.
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Select groups in multiple stages or with multiple constraints that must all be satisfied simultaneously, often requiring case-by-case analysis of different composition scenarios.
Select a committee or group where the composition must satisfy constraints on the number of people from different categories (e.g., men/women, year groups, instrument types) such as 'at least 2 men', 'more women than men', or 'exactly 3 from each category'.
Calculate the probability that a randomly selected committee or group has a specific composition (e.g., exactly k members from category A) using combinations and probability ratios.
Describe or carry out the practical steps to obtain a simple random sample or systematic sample, including use of random number tables, numbered lists, or dice.
| \cline { 3 - 8 } \multicolumn{2}{c|}{} | Score on green dice | ||||||||
| \cline { 3 - 8 } \multicolumn{2}{c|}{} | 1 | 2 | 3 | 4 | 5 | 6 | |||
| 1,2 or 3 | 1 | 2 | 3 | 4 | 5 | 6 | ||
Select items from multiple categories (e.g., books, songs, exam questions from different sections) where specific numbers must be chosen from each category.
Identify problems with a proposed sampling method, explain why it would not produce a random or representative sample, or suggest improvements to a flawed sampling procedure.
Explain, describe, or compare sampling methods (simple random, stratified, systematic, quota, opportunity/convenience) including their advantages, disadvantages, and potential biases.
Calculate the number of individuals to sample from each stratum in a stratified sample, given the stratum sizes and total sample size.
Derive the complete probability distribution for a random variable defined by a selection process (e.g., number of vowels in selected letters, sum of numbers on selected cards).
Calculate probabilities for outcomes over multiple independent trials of a selection process (e.g., probability that an event occurs exactly k times in n trials).
Use the pigeonhole principle to prove that certain configurations must exist when distributing items into containers or selecting from constrained sets.
Select a group where certain individuals have special relationships (siblings, twins, couples) and restrictions apply to whether they can both be included or excluded together.
Arrange people into multiple distinct rows, groups, or positions (e.g., front row and back row, different taxis, different bins) where the groups themselves may be distinguishable or indistinguishable.
Calculate probabilities when items are selected sequentially with or without replacement, often involving conditional probabilities or tree diagrams for multiple selections.
Arrange identical items of different types in a line or row, counting distinct arrangements (e.g., arranging identical packets of different products on a shelf, arranging identical colored items in sequence).
Pack items (often with given weights, sizes, or lengths) into bins or containers with capacity constraints using algorithms like first-fit, first-fit decreasing, or finding optimal packings.
Arrange people or objects in a line or row where certain individuals must be next to each other, or must not be next to each other, or specific groups must stand together.
Calculate conditional probabilities or determine independence/exclusivity of events defined by selection outcomes (e.g., probability of event A given event B occurred).
Arrange letters of a word or set of distinct/identical letters with constraints such as specific letters in specific positions, certain letters together, or letters in alphabetical order.
Count how many numbers can be formed from a set of digits subject to constraints like being even, being in a certain range, having specific digits in specific positions, or using distinct digits.