An interactive explainer for a Year 10 Australian student. Every idea comes with a netball example and something to play with. Pick a depth up top, work through the eight sections, and if you spot anything to fix, use the feedback box at the bottom.
New to itProbability is how likely something is, written as a number from 0 to 1. 0 means it can't happen, 1 means it's certain, and 0.5 is a straight 50-50, like tossing a coin for the first centre pass.
Year 10Probability measures how likely an event is, on a scale from 0 (impossible) to 1 (certain). You can write the same value as a fraction, a decimal or a percentage: 1/2 = 0.5 = 50%. The closer the number sits to 1, the more likely the event.
Going furtherEvery probability sits in the range 0 ≤ P(A) ≤ 1. List every possible outcome (that whole list is the sample space) and the probabilities across it always add up to exactly 1. That single rule is what the rest of this page is built on.
Hover or tap a netball event to see where it sits on the line and why.
0 · impossible0.5 · even1 · certain
Pick an event above.
Knowing 0 to 1 is one thing. Where do those numbers actually come from? For the simple cases, you can just count.
Section 2 of 8
When outcomes are equally likely, you count
New to itIf every outcome is just as likely as every other, the probability is simple: how many ways it can happen, divided by how many things could happen in total.
Year 10For equally likely outcomes, P(event) = favourable outcomes ÷ total outcomes. Drop all 7 bibs in a bag and pull one out without looking. Two of them are shooters (GS and GA), so P(shooter) = 2/7 ≈ 0.29.
Going furtherThis only holds while the outcomes really are equally likely. A weighted die, or a shooter who is better than her teammate, breaks the equal-chance assumption. Once that happens, counting is no longer enough and you need real data, which is exactly the next section.
What's the chance of pulling a
2/7
2 shooters out of 7 bibs = 0.29 = about 29%
Counting works when you know every outcome is equal. But how good is a shooter really? For that, you can't count. You have to take the shots.
Section 3 of 8
Measure it: take the shot, then take a hundred more
New to itYou don't always know the real chance. So you try it lots of times and see how often it happens. Take just a few shots and your result can be all over the place. Take hundreds, and it settles close to the true chance.
Year 10Experimental probability = times it happened ÷ number of trials. It is what you measure, not what you calculate. Theoretical probability is the true underlying chance. A short run can land far from it; a long run settles near it. Set the shooter's true rate below, then compare a few shots against a few hundred.
Going furtherThat settling has a name: the law of large numbers. Each shot is one random trial, so a short run can be lucky or unlucky, but as the number of trials grows the measured rate converges on the true probability. It says nothing about the next single shot, only about the long-run average.
0
goals
0
shots taken
–
experimental
0.75
theoretical (true)
–
gap
experimental rate so far the true rate
A shooter either scores or she misses. Those two chances are joined at the hip, and that link is a shortcut worth having.
Section 4 of 8
Score or miss: the two add up to 1
New to itEither she scores or she misses, and one of them has to happen. So the two chances add up to 1. That means the chance of a miss is just 1 minus the chance of a goal.
Year 10The complement of an event A is "A does not happen". P(not A) = 1 − P(A). If P(goal) = 0.75, then P(miss) = 1 − 0.75 = 0.25. Slide the rate and watch the two halves stay tied together.
Going furtherComplements are the fast lane for "at least one" problems. Rather than adding up every way something can happen, work out the single way it does not, and subtract from 1. You will use exactly this trick in the next two sections.
P(goal) 0.75
P(miss) 0.25
P(miss) = 1 − 0.75 = 0.25
One shooter is simple. Now put the GS and the GA together. What are the odds they BOTH score?
Section 5 of 8
Both shooters score: multiply
New to itTwo things that don't affect each other. To get the chance of both happening, multiply their chances together.
Year 10Two events are independent when one does not change the other. For independent events, P(A and B) = P(A) × P(B). If the GS scores 80% and the GA scores 60%, then P(both score) = 0.8 × 0.6 = 0.48. The tree below lays out all four outcomes, and their probabilities always add to 1.
Going furtherIndependence is the catch. If the GA only shoots when the GS has been fouled off the ball, the two are linked and multiplying is wrong. For "at least one of them scores", use the complement: 1 minus P(both miss).
P(both score) = 0.48P(at least one) = 0.92P(neither) = 0.08
"Both" means multiply. But what about "this OR that"? Adding is close, but there's a trap when they can overlap.
Section 6 of 8
This or that, and the two-way table
New to itSometimes you want the chance of one thing OR another. If they can't both happen at once, just add. If they can overlap, add them and then take off the overlap, so you don't count it twice.
Year 10Mutually exclusive events cannot happen together, so P(A or B) = P(A) + P(B). When they can overlap, P(A or B) = P(A) + P(B) − P(A and B). A two-way table makes this painless: the totals you need are sitting in the margins. Tap a question below to light up the cells it uses.
Going furtherThe subtraction is there because the overlap gets counted once inside P(A) and again inside P(B). Mutually exclusive is simply the special case where the overlap is 0, so there is nothing to take off. Drawing one bib and asking "GS or GA" is mutually exclusive; asking "a GS shot or a goal" is not, because a GS goal is both.
Goal
Miss
Total
GS
18
4
22
GA
9
5
14
Total
27
9
36
Tap a question to see which cells it reads and how the fraction is built.
You can read chances off a table. Now flip it around: if you know the chance, how many goals should you actually expect?
Section 7 of 8
How many goals to expect
New to itIf you know the chance of a goal and how many shots she takes, you can estimate how many goals to expect. Just multiply the two.
Year 10Expected number of outcomes = number of trials × probability. 40 shots at 75% gives an expected 40 × 0.75 = 30 goals. It is an average, so the real total in any one game will bounce around that number rather than land on it exactly.
Going furtherTurn each shot into points and you get expected value, the tool a coach actually uses. In Suncorp Super Netball a shot from the outer ring in the last five minutes of a quarter is worth 2 points. Expected points per shot = probability × points. An 80% inner shot is worth 0.8 points on average; a 50% Super Shot is worth 1.0. That comparison is the whole decision.
Expect about 30 goals (40 × 0.75)
Stretch: which shot is worth more? (Super Shot is 2 points)
Inner: 0.80 pts per shotSuper: 1.00 pts per shotTake the Super Shot
That's the whole toolkit. Five quick netball questions to see what stuck.
Section 8 of 8
Quick quiz
Pick an answer. It tells you straight away, with the reason.
Spot a mistake, or got feedback for Mike?
Type anything: what's wrong, what's confusing, what to add or cut. Then hit copy and paste it into a chat with Claude to get version two.