Level 5: Probability rules

Probability · level 5 of 8 · rough age 12-13 (a guide for parents; anyone can start anywhere)

In level 4 you found chances by listing every outcome in a table or a tree. That works until the list gets too long. In this level you learn the rules that let you combine chances without listing everything: when to add, when to multiply, how to handle overlaps, and the trick of working out the opposite. Each rule comes with a reason, so you know when it is allowed. The level ends with the most famous wrong idea about chance, and what independence really means.

Lesson	You will be able to
Mutually exclusive events and "or"	Tell whether two events can happen together, and add their chances when they cannot
The general addition rule	Find P(A or B) for any two events by taking away the overlap, using Venn diagrams and tables
The multiplication rule	Find P(A and B) for independent events, and for draws with and without replacement
"At least one"	Use the complement to find the chance of at least one success, and solve de Méré's dice puzzle
Trees with unequal branches	Draw and read a tree where the chances change from stage to stage, and check it adds to 1
The gambler's fallacy and the hot hand	Explain why chance has no memory, why long streaks are normal, and when the past really does matter

Previous: Level 4: Two things at once · Next: Level 6: Conditional probability · Probability topic page