Why the tree diagram is fundamental to studying probability - and why it should be introduced right from the start.

Progression from natural frequencies to proportions to the multiplication rule, and hence to probability trees.

Moving from the particular to the general, then revisiting the particular in that light, and so generalising further.

Representing frequencies and probabilities diagrammatically, and using the diagrams as interpretive tools.

When are events independent of each other? Sampling with and without replacement.

Understanding statistics about testing for cancer or the chance that two babies in a family could die of SIDS is a crucial skill for ALL students.

A practical experiment which will introduce students to tree diagrams, and help them to understand that outcomes may not be equally likely.

A practical experiment which uses tree diagrams to help students understand the nature of questions in conditional probability.

A practical experiment provides data. Moving onto expected results provides a context to establish the multiplication rule in probability, and an intuitive approach to conditional probability.

What's the fairest way to choose 2 from 8 potential prize winners? How likely are you to be chosen?

Who's closest to the correct number of sweets in a jar - an individual guess or the average of many individuals' guesses? Which average?

How do scientists or mathematicians estimate the size of a population of wild animals?

What proportion of people make 90% confident guesses which actually contain the correct answer?

Should Louis go for the safer options, hoping to limit his losses, or would he be better off with a riskier strategy, focusing on maximising his profit?

Should you insure your mobile phone? It rather depends on whether you focus on the long-term pay-off or the effect of a single event.