Probability · Basic probability
Chapter 1 · 4
The idea
Sample space & systematic listing
How to list every outcome once and only once — systematic listing, two-way sample-space diagrams, the product rule for counting, and why swapping two things over sometimes makes a new outcome and sometimes doesn't.
A full journey — read it, play with it, work it, then earn real exam marks. Everything stays on the timeline below.
In this lesson — start anywhere
Probability · Basic probability
Sample space & systematic listing
How to list every outcome once and only once — systematic listing, two-way sample-space diagrams, the product rule for counting, and why swapping two things over sometimes makes a new outcome and sometimes doesn't.
Why it works
Counting is the whole topic
When every outcome is equally likely, is favourable outcomes over total outcomes — and both numbers are counts. So this whole topic is one skill: counting the outcomes without missing any and without counting any twice. The complete list of everything that could happen is the sample space."Systematic" is the whole game
Ask someone to list the outcomes of flipping three coins and they will write HHH, HHT, THH, TTT, then stare at the page. Scribbling outcomes as they occur to you gives no way of knowing when you've finished. Instead, fix one thing and run through all the others, then change the fixed thing:Keep reading — free
The rest of the explanation, plus 3 worked examples you step through move by move.
Start freeTakes a minute — no card.