Tree and total probability rule (two events)

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I'd like to know if the tree related to the following rule: enter image description here

is the first or the second one or can be both depends on the context. If possible, make some example.

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I suppose the second tree is enough to heuristically illustrate the rule, but may lead the reader into thinking B occurs with probability 1. The first tree is more complete since it is exhaustive: it shows all possible states of the world.