How many false positives across many null tests
You run independent hypothesis tests, each at significance level , and in truth every null is correct (no real effect anywhere).
How many "significant" results do you expect? What is the probability of at least one false positive, and how does a Bonferroni correction fix it?
Show a hint
Under the null a valid p-value is Uniform, so each test rejects with probability exactly , independently. Count the rejections.
Your answer
This one is open-ended. Work it through, then check your reasoning against the full solution.