Probability that automated process is 95% accurate given n sucesses

Question

I have trained a robot to flip an (unbiased) coin and get heads every time. Each flip is with a new coin (more on that shortly). How many successes does the robot need before I can be confident (say 95%) that the robot is trained to do the task?
How will this change if we know a given proportion (say 10%) of coins are biased, making success less likely by chance (say pHEAD=0.3)?

Dedekind Cuts · Answer

For your first question, after $n$ successful flips (assumed independent), the (exact) lower $(1-alpha)$-confidence bound for the probability your robot lands heads is $alpha^{1/n}$. So after 10 flips the 95% confidence bound is $(.05)^{1/10} approx 74%$, after 20 flips it's $(.05)^{1/20}approx 86%$, etc.

Answered by Dedekind Cuts on December 15, 2021

Probability that automated process is 95% accurate given n sucesses

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