Apply and interpret the general Multiplication Rule with conditional probability.
Find a compound event probability by multiplying along each path and adding disjoint paths
Problem
In the tree, exactly one head and one tail occurs along paths \(\mathrm{HT}\) and \(\mathrm{TH}\). Compute each path probability and add the two disjoint paths.
Exactly one head and one tail can occur along two different ordered paths. We’ll identify both successful routes, multiply along each fair-coin path, verify that the routes are disjoint, and add their probabilities so neither valid order is omitted.
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