At least there steel some cake on the knife

Given an event E and a system S , if S operates successfully with absolute certainty in any given percentage p of all trials, then:

P(S=1|E) = 1 & P(E) = p

Therefore, by the The Fantana Theorem, assuming failure outside E:

P(S=1) = P(S=1|E) • P(E)

=(1.00)(p)

P(S=1) = p

Q.E.D.

Corollary: The system is infallible whenever it works, which occurs precisely at any given percentage of the time.

In simpler terms (using Fantana’s exact words, in the first known expression of his theorem to state the efficacy of his methods):

“Sixty percent of the time, it works every time.”

Edit: spelling