Chance language
Chance language (certain/possible/impossible; likely/unlikely); intuitively compare the likelihood of events.
Chance language is the everyday vocabulary we use to talk about whether something will happen: certain, possible, impossible, likely, unlikely. It is the first, word-based step toward the numbers of probability.
What it means
An event is something that might or might not happen — rolling a six, rain tomorrow, the sun rising. Chance language sorts events by how sure we can be:
- Certain — it will happen, no matter what. The sun will set today.
- Impossible — it cannot happen, ever. You roll an ordinary die and get a 7.
- Possible — it might happen; it is neither certain nor impossible. Most events sit here.
Within “possible”, we compare how sure we are:
- Likely — it will probably happen, more often than not.
- Unlikely — it will probably not happen, but it still could.
- Even chance — it is just as likely to happen as not, like a coin landing heads.
Picture a line from impossible on the left to certain on the right, with even chance in the middle. Every event has a spot on that line. “Likely” sits toward the right; “unlikely” toward the left. You do not need numbers yet — you compare events by asking “which spot is further right?” To decide, count the ways an event can happen against the ways it cannot. A bag with 9 red marbles and 1 blue: drawing red is likely, because most of the marbles are red.
Worked examples
1. Sort these events. Rolling a standard six-sided die:
| Event | Likelihood |
|---|---|
| You roll a number from 1 to 6 | certain |
| You roll an 8 | impossible |
| You roll a 4 | possible (unlikely — 1 way out of 6) |
| You roll an even number | even chance (3 ways out of 6) |
2. Compare two bags. Bag A holds 8 red, 2 blue. Bag B holds 5 red, 5 blue. Drawing blue is more likely from Bag B, because half its marbles are blue versus only a fifth in Bag A.
3. Spinner talk. A spinner is three-quarters green, one-quarter yellow. Landing on green is likely; landing on yellow is unlikely; landing on red is impossible (there is no red).
The generative-art connection
Chance is where art stops being fully planned and starts to grow. In generative art you write a rule, then let chance fill in the choices — and the likelihood you pick controls what you see. Make each new dot likely green and unlikely yellow, and a mostly-green field appears, speckled with rare yellow: the look of the picture is the likelihood made visible.
Build a spinner in the Math Learning Center apps and spin it many times, tallying results — a big green slice fills up fast, a thin yellow slice barely grows. Then watch Seeing Theory let a chance event repeat hundreds of times: unlikely things really do show up, just seldom. The art teaches the words back to you — “likely” is a slice that keeps winning, “impossible” is a colour that never appears.
Common misconceptions
- “Unlikely means it won’t happen.” Unlikely still can happen — rare is not impossible. Only impossible means never.
- “Possible means 50-50.” Possible just means “not ruled out.” A possible event can be very likely or very unlikely.
- “It didn’t happen last time, so it’s due.” Each spin or roll forgets the last one. Past results do not change how likely the next one is.
What a learner should be able to solve
The benchmark for mastering this concept — the problems a child at this stage is expected to be able to work through.
-
Sort each event as `certain`, `impossible`, or `possible`: (a) tomorrow is a day of the week; (b) a cat you meet says a full sentence in English; (c) the next person to walk past is wearing red; (d) you pick a month with the letter `r` in its name from the 12 months.
Answer
(a) certain — every tomorrow has a weekday name. (b) impossible — cats do not talk. (c) possible — some people wear red, some do not. (d) possible — 8 of the 12 months contain `r` (only May, June, July, August do not), so it can happen but is not certain.
Art hook A row of 4 event-cards on a canvas; clicking a card drops it into one of three coloured bins (green = certain, red = impossible, grey = possible), each bin a labelled column so the sort becomes a visible layout.
-
A bag has `3` red counters and `7` yellow counters. You take one without looking. Is drawing yellow `likely` or `unlikely`? Explain by counting the ways.
Answer
Likely. There are `7` ways to draw yellow and only `3` ways to draw red, so yellow happens more often than not.
Art hook Draw 10 dots in a grid, 3 red and 7 yellow. A 'draw' button lights up one random dot; a running tally-bar for red vs yellow grows over many draws so the yellow bar visibly outpaces the red.
-
Put these four spinner events in order from `least likely` to `most likely` on a chance line. A spinner is `half` blue, `one-quarter` green, `one-quarter` white, and has no pink at all: landing on pink, landing on green, landing on blue, landing on a colour (any).
Answer
Least → most: pink (impossible, `0`) → green (`¼`) → blue (`½`) → any colour (certain, `1`). Green and white are equal quarters, but blue's half beats green's quarter, and 'any colour' always happens.
Art hook Draw the spinner as a pie (half blue, quarter green, quarter white) beside a horizontal line labelled impossible→certain; the learner drags each event-label onto the line, and it snaps to the fraction of the pie that colour fills.
-
Find the mistake. Sam says: 'It is unlikely to rain tomorrow, so it definitely will not rain.' What is wrong with Sam's thinking?
Answer
Unlikely does not mean impossible. Rain probably will not come, but it still can — only `impossible` means it can never happen.
Art hook A cloud that, on a button press, rains with a small chance each press; a counter shows most presses are dry but occasionally rain falls — the rare event appearing on screen disproves 'definitely not.'
Training exercises
Practice problems, easier first, that build toward the bar above. Each doubles as a seed for an interactive artwork.
-
Match each event to one word: `certain`, `possible`, or `impossible`. (a) The sun will rise tomorrow. (b) You will grow wings by lunchtime. (c) You will eat something today.
Answer
(a) certain, (b) impossible, (c) possible (very likely for most people, but not guaranteed).
Art hook Three glowing badges (green/grey/red) that a child taps to tag each event; correct tags make the badge pulse once.
-
Which is more likely: rolling a number less than `7` on an ordinary six-sided die, or rolling exactly a `2`?
Answer
Less than `7` is more likely — it is certain (all 6 faces are under 7), while a `2` is just 1 face out of 6.
Art hook Six die-face dots arranged in a ring; highlight all faces matching the event so 'less than 7' lights the whole ring and 'a 2' lights only one — the amount of light is the likelihood.
-
A coin is flipped. Is landing on heads `likely`, `unlikely`, or an `even chance`? Why?
Answer
Even chance — there are 2 equally possible sides, so heads is just as likely as tails.
Art hook A coin that flips with a spin animation; a two-bar tally (heads/tails) that stays roughly equal over many flips, showing 'even chance' as two bars growing side by side.
-
A bag has `1` red marble and `9` green marbles. Is drawing red `likely` or `unlikely`? How many ways can you draw red, and how many green?
Answer
Unlikely. There is `1` way to draw red and `9` ways to draw green, so green happens far more often.
Art hook Ten dots, 1 red among 9 green; each 'draw' flashes a random dot — the red one is caught only rarely, making 'unlikely' something you feel by waiting for it.
-
Bag P has `4` blue and `4` yellow. Bag Q has `6` blue and `2` yellow. From which bag are you more likely to draw blue?
Answer
Bag Q — blue is `6` out of `8` there (most of the bag), versus `4` out of `8` (half, an even chance) in Bag P.
Art hook Two dot-grids side by side, each 8 dots coloured by bag; a button draws from each and stacks blue-vs-yellow tally columns so Q's blue column climbs faster.
-
Order these three events from `least likely` to `most likely`: rolling a `6` on a die, flipping heads on a coin, the sky being blue at some point this week.
Answer
Least → most: rolling a `6` (`1` in `6`) → flipping heads (`1` in `2`) → blue sky this week (as good as certain).
Art hook Three markers a learner drags onto a left-to-right chance line (impossible→certain); the markers snap to positions matching 1-in-6, 1-in-2 and near-certain, drawing the number line as a likelihood ruler.
-
A spinner is split into `5` equal parts: `3` red, `1` blue, `1` green. Name one event that is `likely`, one that is `unlikely`, and one that is `impossible` on this spinner.
Answer
Likely: landing on red (`3` of `5` parts — more than half). Unlikely: landing on blue (only `1` of `5`, less than half). Impossible: landing on yellow (there is no yellow at all).
Art hook A 5-slice pie spinner (3 red, 1 blue, 1 green); spinning tallies each colour, and a fourth 'yellow' tally that never moves makes 'impossible' visible as a bar stuck at zero while the red bar runs ahead.
-
Design your own bag of `10` counters so that drawing red is `likely` but not `certain`. How many red counters would you use, and why not `10`?
Answer
Any count from `6` to `9` red works — more than half makes red likely, but fewer than `10` leaves at least one non-red counter, so red stays possible (not certain). Example: `8` red, `2` blue.
Art hook An empty 10-dot grid the child fills by clicking to add red dots; a live label reads 'unlikely / even chance / likely / certain' as the red count crosses 5 and 10, turning a design choice into a chance readout.
-
Find the mistake. Aria flips a coin and gets tails four times in a row. She says: 'Heads is due now, so the next flip is more likely to be heads.' Is she right?
Answer
No. Each flip is a fresh even chance — the coin does not remember past flips, so the next flip is still `even chance`, not more likely to be heads.
Art hook A coin-flip stream that logs the last results as a row of H/T tiles; a meter always reads 'even chance' for the next flip no matter the streak, showing chance has no memory.
-
Here are five events. Sort them into `impossible`, `unlikely`, `even chance`, `likely`, `certain` (one each): (a) picking a vowel from the letters of `CAT`; (b) a tossed coin landing heads; (c) rolling a whole number from `1` to `6` on a die; (d) rolling a `7` on that die; (e) drawing red from a bag of `9` red and `1` white.
Answer
(a) unlikely — 1 vowel (A) out of 3 letters. (b) even chance. (c) certain — all faces are 1–6. (d) impossible — no 7 on the die. (e) likely — 9 of 10 are red.
Art hook Five event-cards the learner drops onto a chance line with five labelled zones; each card, once placed, draws its own tiny visual (letters, coin, die, dots) so the whole line becomes an illustrated likelihood strip.