How likely? It lives on one line.

One line, five honest words.

Mathematicians measure chance from 0 to 1. Nothing can be more impossible than 0, and nothing can be more certain than 1 — so every probability you'll ever meet fits somewhere in between. We hang a few familiar words on the line to describe the regions: impossible, unlikely, even chance, likely, and certain.

The exact middle, 0.5, has a special name: an even chance (or "fifty-fifty"). It means a thing is just as likely to happen as not — like a fair coin landing heads. Drag the handle below and watch the marker travel the scale, while the word underneath updates to match where you are.

One thing the line quietly insists on: probabilities can never escape past the ends. You can't have a chance of 1.5 or −0.2, because nothing is "more than certain" or "less than impossible." So if you ever calculate a probability and get a number bigger than 1 or smaller than 0, that's a red flag — a sign to go back and check your working, not a strange new kind of luck. Every honest probability has to land somewhere on this single stretch of line.

Fraction, decimal, percent — all the same.

You just saw it on the slider: one probability can be dressed three ways, and they're completely interchangeable. A coin's chance of heads is ½ as a fraction, 0.5 as a decimal, and 50% as a percent. Three costumes, one value.

Here's how to hop between them. A fraction like ½ literally means "1 out of 2." To get the decimal, you divide the top by the bottom: 1 ÷ 2 = 0.5. To get the percent, you multiply the decimal by 100 and add a "%" sign: 0.5 × 100 = 50%. Percent even means "per hundred," so 50% is just "50 out of every 100."

So whenever a question gives you a percent and your working is in fractions, you're allowed to switch — they're equal. Pick whichever outfit makes the maths easiest, then change back at the end if you need to.

Drop everyday events onto the line.

Time to use your judgement. Below are six everyday events. Your job: put each one where it belongs on the probability scale — far left if it's basically impossible, dead centre if it's a coin-flip, far right if it's as good as certain.

Drag a card onto the line with your finger or mouse — or, to place one with a click, tap a card to select it, then tap one of the five zone buttons. The line will tell you whether your spot makes sense.

How do you decide where a card goes? You don't need a formula for most of these — you need judgement. Ask yourself two questions: "Could this ever not happen?" (if no, it's near certain, on the right) and "Could this ever happen at all?" (if no, it's at 0, on the far left). Everything else slots in between, with a coin-flip as your anchor at the middle. The point isn't to hit a perfect pixel — it's to feel, in your hands, that "likely" and "unlikely" are really just regions of one line.

Notice how the two trickiest cards behave. "It rains at some point this year" feels certain, but unless you live somewhere it truly rains every year, the honest spot is "very likely" rather than dead on 1 — so we keep that one a little generic, because the real answer depends on where you live. And "rolling a 7" isn't just unlikely, it's impossible: a normal die has no 7, so its chance is exactly 0.

Favourable ÷ total.

For a fair setup — where every outcome is equally likely — you don't have to guess the probability at all. You count. The recipe is one short line:

"Favourable" just means the outcomes you're hoping for. "Total" means every outcome that could happen. Count the winners, count everything, divide. That's it.

There's one important catch, and it's worth saying out loud: this counting trick only works when every outcome is equally likely. A fair coin, a fair die, an evenly-divided spinner — each side or face has exactly the same chance, so plain counting is fair. If the die were secretly weighted, or a spinner had one giant sector and three tiny ones, the outcomes wouldn't be equal, and "favourable ÷ total" would quietly lie to you. So before you count, always ask: are these outcomes really equal? When they are, the recipe is rock-solid.

Try it yourself below. Pick a device, then tap the outcomes you'd count as a "win." The calculator counts your favourable outcomes over the total and shows the chance as a fraction, a decimal and a percent — and drops it onto the scale so you can see its zone.

Every chance in the bag adds up to 1.

Here's a rule that quietly checks all your work: the probabilities of all the possible outcomes always add up to 1. That makes sense — something has to happen, and "something happens" is certain, which is 1.

A fair die has six faces, each with probability ⅙. Add them up: ⅙ + ⅙ + ⅙ + ⅙ + ⅙ + ⅙ = 6/6 = 1. A coin has two sides at ½ each: ½ + ½ = 1. The whole line of possibilities, stacked end to end, fills exactly one unit:

This gives you a brilliant shortcut. The chance an event doesn't happen is just 1 minus the chance it does. If the chance of rain is 0.7, the chance of no rain is 1 − 0.7 = 0.3. If the chance of rolling a 6 is ⅙, the chance of not rolling a 6 is 1 − ⅙ = ⅚. Sometimes counting the "not" is far easier than counting the "yes" — and this rule lets you swap between them for free.

"A 1-in-6 chance means it lands every 6 rolls." (Nope.)

This is the slip almost everyone makes. If a six has a probability of ⅙, it's tempting to think you'll get exactly one six in every six rolls, like clockwork. But the die has no memory and no schedule. ⅙ is a long-run tendency, not a guarantee — it tells you what to expect on average over many, many rolls, not what happens in the next six.

You might roll six times and see zero sixes. Or two sixes. Or, rarely, all sixes. Each roll is its own fresh ⅙, completely unbothered by the rolls before it. The "one in six" only shows up clearly when you zoom out to hundreds or thousands of rolls.

The probability we calculate (⅙) is called theoretical probability. The fraction you actually get by rolling — sixes ÷ rolls — is called experimental probability. Roll a few times and they barely match. Roll a lot, and the experimental fraction creeps toward the theoretical ⅙. Try it:

Experimental probability isn't just a way to check the theory — sometimes it's the only tool you've got. What's the chance a drawing pin lands point-up, or that a particular bus is late? There's no neat fraction to calculate, so you do the experiment: try it many times and use the fraction you measure as your best estimate. The more trials you run, the more you can trust it.

Five questions. No pressure.

Read each one and pick the answer you think fits. Guessing is allowed — that's how the pattern sticks.