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I am playing a game where I randomly get 1 of 6 different prizes whenever I do a certain action. The 6 prizes do not drop at the same rate. Some are more rare than others. I am trying to figure out the percent chance that each prize is given. I have been keeping track of all my attempts for a few weeks, so I have a fairly good idea, but I would like to know how to calculate my confidence level.

For example, lets say that I have received 100 prizes and 8 of them have been a certain kind. I would say that I have an 8% chance to get that prize on each future attempt. What I want to know is how to calculate the error range or confidence level of that 8%. Is that really 5%-11%? How many samples do I need to get the error down to under 1%?

I never took a statistics class, so Im new to this kind of math. Thanks!

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The formula you want is $$\delta p = \sqrt\frac{p(1-p)}{n}$$ which comes from the variance of a Bernoulli distribution. So if your observed fraction is $p = 0.08$ with $n=100$ observations, the error bar on $p$ is $\delta p = \sqrt((0.08)(1 - 0.08)/100) = 0.03$, so you would report $p = (8 \pm 3)\%$. That's a 1-$\sigma$ error bar; you can scale it up if you require a higher confidence level.

To find the $n$ you'll need to obtain a given $\delta p$, just use algebra to solve for $n$. If by 1% error you mean $\delta p = 0.01$, you get $n \approx 730$. If by 1% error you mean $\delta p / p = 0.01$, you get $n \approx 110000$.

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