Conditional probability and tree diagrams

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Learn it For two events in a row, multiply along the branches of a tree diagram. Without replacement, the second probability changes. P(A given B) = P(A and B) ÷ P(B): only look at the cases where B happened.

Example: A bag has 5 red and 3 blue marbles. Two are drawn without replacement. P(both red)?

First red: 5/8. Second red: 4/7.
5/8 × 4/7 = 20/56 = 5/14.

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