@FreelanceReinh wrote:
Equality of these two p-values would occur for the symmetric binomial distribution, i.e., p=0.5, if, in addition, the observed frequency is the expected value np, which requires an even n.
These conditions are sufficient, but not necessary for the equality. There are many other examples, e.g., n=5, 1 success observed, p such that (1-p)**5=1-(1-p)**5-5*p*(1-p)**4 -- this equation has the unique solution p=0.216105706313... in [0, 1]. Both one-sided p-values are then 0.7040028597...

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