tree diagram
tree diagram articles on the Math Mental blog, with worked examples solved step by step.
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Two-leg knockout probability: trees and penalties
To find the chance a team advances in a two-leg tie, list every combination of results across both matches (win, draw or loss in each), multiply the probabilities along each path (the product rule, assuming the matches are independent) and add the paths that lead to qualification. Paths that end level on aggregate go to penalties: multiply the chance of getting there by the chance of winning the shootout. In the hypothetical example below, Team A advances with probability 0.565, or 56.5%.
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