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Problems in GARP's 2020 FRM material

Hi! I have a concern about QA chapter 9 answer to the question 9.4, which says that the probability of including a single irrelevant regressor is 1 - alpha, where alpha is the test size. But shouldn't it actually be alpha? As I am understanding this is that including the irrelevant regressor is incorrectly rejecting the true 0-hypothesis, which is a Type 1 error and the probability of that is equal to the test size. Or am I missing something?