Binomial Distribution Calculator

  Enter the value for p :  

  Enter the value for n :  

  Enter the value for i  :  

  Probability (Number of Successes = i) :-

  Probability (Number of Successes <= i) :-

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About Binomial Distribution

If n independent trials, each of which results in a “success” with probability p and in a “failure” with probability1-p, are to be performed and if X representsthe number of successes that occur in the n trials, then X is said to be a binomial random variable with parameters (n, p).The probability mass function of a binomial random variable with parameters n and p is given by :-     P{X = i} = ⁿC_i  pⁱ(1-p)^(n-i)
Therefore, the binomial distribution function can be obtained by just summing the mass function from k = 0 to k = i :-
P{X <= i} = ∑ⁱ_(k=0)  ⁿC_i  p^k(1-p)^(n-k)