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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.