Calculate Probability Error for 100 Exp: Sample Size of 15

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SUMMARY

The discussion focuses on calculating the probability error for a sample size of 100 experiments with 15 unfavorable events. The participants suggest using a binomial distribution to model the observed number of failures, emphasizing that the independence of experiments is crucial. For improved accuracy in estimating uncertainty, the Feldman-Cousins method is recommended. Additionally, the Central Limit Theorem (CLT) can be applied for constructing confidence intervals for the number of failures.

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  • Understanding of binomial distribution and its properties
  • Familiarity with the Feldman-Cousins method for confidence intervals
  • Knowledge of the Central Limit Theorem (CLT)
  • Basic statistical concepts related to probability and error analysis
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I have a sample size of 100 experiments out of which 15 are unfavorable events. I do this measurement for different initial conditions of my experiment. The sample size remains constant but the no. of unfavorable events change in each case.

I calculate the probability of success in each case but I want to know the error in this calculation of probability and plot it as error bars in my graph.

How to proceed ?
 
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For a fixed (unknown) probability of failure your observed number will follow a binomial distribution, if all 100 experiments are independent of each other.
If you use your observed events to calculate the uncertainty, the result is not exact but unless you have very small numbers of failed experiments the difference will be small. Feldman Cousins would be better in that case.
 
Maybe you (OP) are trying to construct a confidence interval for the number of failures? Maybe you can use the CLT for the sampling means of experiments 1 through n?
 

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