Probability · Combined events & tree diagrams
Chapter 1 · 4
The idea
Probability without replacement
Why the second pick happens in a smaller, changed bag — so the total always drops by one but a colour's count drops only if that colour was taken — and how that turns "one of each", "at least one" and the reverse quadratic questions.
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 · Combined events & tree diagrams
Probability without replacement
Why the second pick happens in a smaller, changed bag — so the total always drops by one but a colour's count drops only if that colour was taken — and how that turns "one of each", "at least one" and the reverse quadratic questions.
Why it works
One sentence, two consequences
Without replacement means the first thing you take is not put back before you take the second. That one sentence is the whole topic — but it has two consequences, and almost everybody remembers only one of them. Work with a real bag throughout: 5 red counters and 3 blue, in total, two taken one after the other.Multiply along a path — it's just counting
Think of the two picks as an ordered pair. There are counters you could take first and, whichever one it was, left to take second: equally likely pairs. Red-then-red pairs: reds to take first, then reds still in the bag, so . HenceKeep reading — free
The rest of the explanation, plus 3 worked examples you step through move by move.
Start freeTakes a minute — no card.