Statistics · Probability
Chapter 1 · 3
The idea
Tree diagrams and sequential events
Using a tree diagram for two-stage experiments: multiply probabilities ALONG the branches of a path (AND), add across the paths that make up an event (OR), and use 1 − P(none) for "at least one". The crucial distinction between sampling WITH replacement (probabilities stay the same) and WITHOUT replacement (the totals, and so the later probabilities, change).
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Statistics · Probability
Tree diagrams and sequential events
Using a tree diagram for two-stage experiments: multiply probabilities ALONG the branches of a path (AND), add across the paths that make up an event (OR), and use 1 − P(none) for "at least one". The crucial distinction between sampling WITH replacement (probabilities stay the same) and WITHOUT replacement (the totals, and so the later probabilities, change).
Why it works
Stage by stage
Take two counters from a bag, one after the other, and the second draw's chances depend on what the first took away — probabilities that *unfold in stages* need a map, and the tree diagram is that map. It lays out a two- (or more) stage experiment stage by stage: from each point, the branches show the possible outcomes of the next stage with their probabilities, and the branches leaving any one point always sum to .Keep reading — free
The rest of the explanation, plus 4 worked examples you step through move by move.
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