Systematic Listing
Systematic listing transforms probability from guesswork into organized counting. When students flip 2 coins and list only HH, HT, TT (missing TH), they're missing 25% of the sample space and getting incorrect probability calculations.
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Why it matters
Systematic listing builds the foundation for accurate probability calculations that students encounter in CCSS.7.SP and LK20.10 curricula. In real-world applications, this skill prevents costly errors: quality control managers listing 36 possible outcomes when testing two production batches, sports analysts calculating 64 tournament bracket possibilities, or epidemiologists tracking 16 possible gene combinations in medical research. Students who master systematic listing at age 12-13 perform 40% better on advanced probability assessments. The method's organized approach—whether using tables, tree diagrams, or ordered lists—ensures no outcomes are overlooked, making probability calculations reliable and mathematically sound.
How to solve systematic listing
Systematic Listing
- List all possible outcomes in an organised way.
- Use a table, tree diagram, or ordered list.
- Count the total number of outcomes.
- Use the list to find probabilities.
Example: Two dice: list all 36 pairs from (1,1) to (6,6).
Worked examples
List all outcomes of flipping a coin.
Answer: H, T
- Identify possible outcomes → Heads (H), Tails (T) — A coin has two sides.
- Write the sample space → S = {H, T} — 2 possible outcomes.
List all outcomes of rolling a 6-sided die.
Answer: 1, 2, 3, 4, 5, 6
- List each face → 1, 2, 3, 4, 5, 6 — A 6-sided die has faces numbered 1 to 6.
- Count → 6 outcomes — There are 6 possible outcomes.
List all outcomes of flipping 2 coins.
Answer: HH, HT, TH, TT
- Systematically list: first coin × second coin → HH, HT, TH, TT — For each outcome of the first event, list all outcomes of the second (and third, if any).
- Count → 4 outcomes (2 × 2 = 4) — The total is the product of individual outcome counts.
Common mistakes
- ✗Missing outcomes when listing compound events. Students write HH, HT, TT for 2 coins instead of HH, HT, TH, TT, calculating probability as 1/3 instead of 1/4.
- ✗Confusing order in compound events. Students list (1,2) but forget (2,1) when rolling 2 dice, getting 21 outcomes instead of 36.
- ✗Inconsistent notation mixing letters and numbers. Students write H1, T2, Head-3 instead of systematic HH, HT, TH, TT format.
- ✗Double-counting identical outcomes. Students count HT twice as 'heads first' and 'tails second,' inflating sample space from 4 to 6 outcomes.
Practice on your own
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