03.M07.03 - Probability Trees - Wrap-Up (Conditional Probability and Independence).pdf

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03.M07.03 - Probability Trees probability tree (display tool) - is particularly useful for showing probabilities when the events occur in stages and conditional probabilities are involved. There are two important things to note here: 1. The probabilities in the first branch-off are non-conditional probabilities P(C) = .4, P(not C) = .6. However, the probabilities that appear in the second branch-off are conditional probabilities. The top two branches assume that C occurred: P(V | C) = .9, P(not V | C) = .1. The bottom two branches assume that not C occurred: P(V | not C) = .3, P(not V | not C) = .7 2. The second thing to note is that probabilities of branches that branch out from the same point always add up to one. The following "bare" tree is missing the appropriate probabilities in each of its branches. Complete them.
Comment Following one branch to a connected branch, such as C then V, represents the occurrence of one event and then another, which requires multiplication of probabilities. Including outcomes reached via either of two end-branches represents the occurrence of one event or another, which requires addition of probabilities.

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