Probability to pass multiple studies [Power / Sample Size]

Dear all (and esp. our expert in probability zizou),

say, we have $$\small{n}$$ studies, each powered at 90%. What is the probability (i.e., power) that all of them pass BE?

Let’s keep it simple: T/R-ratios and CVs are identical in studies $$\small{1\ldots n}$$. Hence, $$\small{p_{\,1}=\ldots=p_{\,n}}$$. If the outcomes of studies are independent, is $$\small{p_{\,\text{pass all}}=\prod_{i=1}^{i=n}p_{\,i}}$$, e.g., for $$\small{p_{\,1}=\ldots=p_{\,6}=0.90\rightarrow 0.90^6\approx0.53}$$?
Or does each study stand on its own and we don’t have to care?

Dif-tor heh smusma 🖖
Helmut Schütz

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