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Addition and Multiplication Rules

Addition and Multiplication Rules. Tree Diagrams. Tree Diagrams. A tree diagram helps us think through conditional probabilities by showing sequences of events as paths that look like branches of a tree.

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Addition and Multiplication Rules

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  1. Addition and Multiplication Rules Tree Diagrams

  2. Tree Diagrams • A tree diagram helps us think through conditional probabilities by showing sequences of events as paths that look like branches of a tree. • Making a tree diagram for situations with conditional probabilities is consistent with our “make a picture” mantra.

  3. Tree Diagrams • The first branch of our tree separates people according to their drinking habits. We label each branch of the tree with a possible outcome and it’s corresponding probability. • What do all the probabilities add up to?

  4. Tree Diagrams • Because the probability of having an alcohol-related accident depends on one’s drinking behavior. Because the probabilities are conditional, we draw the alternatives separately on each branch of the tree.

  5. Tree Diagrams • What’s the probability of getting in an accident? • What’s the probability of not getting into an accident? • What’s the probability of getting into an accident given that the alcohol consumption was moderate?

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