# If I know the probability of something happening after n trials is X, how can I estimate the probability of it happening for each individual trial.

This is assuming each trial has an independent probability.

In other words, lets say that I perform $50$ trials a $100$ times. I know that the event happened only in $5\%$ of those hundred $50$-trial sets. How can I estimate the probability of it happening in any given single trial?

Also, this probably has a well known name and solution. I would be happy to be pointed to it and reading more.

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We assume that the only information that has been recorded is whether or not the event happened or did not happen in the various $50$-trial rounds. If we have more information, such as the total number $N$ of times the event happened in the $5000$ trials, then we make the natural estimate $N/5000$.
Let $p$ be the probability of the event happening in a single trial. Then the probability it does not happen in $50$ trials is $(1-p)^{50}$.
Our estimate for $(1-p)^{50}$ is $0.95$. So our estimate for $p$ is $1-(0.95)^{1/50}$.