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I'm a novice to DS, so feel free to correct me.

Imagine we have $N$ biased coins each with different probability of getting heads (which are known to us prior). What's the probability of getting $k$ or more heads? Trials are independent and $0<k<N$.

Is there a general or computational method of calculating this? Does it count as Poisson? I'm not quite sure how to incorporate already known probabilities other than writing some code for building a distribution for large number of trials, but there must be a better way, right?

Please name/link concepts as I'm just learning and would love to know more. Thanks in advance.

MaxelRus
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  • There are several threads about this. They vary according to how large $N$ is and what the distribution of the probabilities might be, because approximations (Poisson, Poisson-Binomial, and Normal, among others) are available. – whuber May 12 '22 at 16:17

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