Binomial Distribution Calculator

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Binomial distribution is one of the probability distributions and it is generally used when there are two mutually exclusive results of a trial or an event. The results are usually called Success or Failure and the Binomial distribution calculator is an online tool useful in finding the probability of success on a particular trial.


Example 1: A coin is tossed 5 times. What is the probability of getting exactly 3 heads?

Binomial Probability formula:P = nrC * pr * (1-p)n-r

Here, n=number of events=5

r=number of successful trials=3 

p=probability of success’s on a single trial since it’s a coin, the probability of getting a head is ½ = 0.5 

nrC = (n!)/ [(n-r)!* r!]

è53C = (5!) / [(5-3)!* 3!] = (5!) / (2!* 3!) = 10

Hence è P = 10 * (0.5)3 * (0.5)2

P = 0.31



Example 2: A coin is tossed 10 times. What is the probability of getting exactly 7 tails?

Binomial Probability formula: P = nrC * pr * (1-p)n-r

Here, n=number of events=10

r=number of successful trials=7

p=probability of success’s on a single trial  since it’s a coin, the probability of getting a tail is ½ = 0.5

nrC = (n!)/ [(n-r)!* r!]

107C = (10!) / [(10-7)!* 7!] = (10!)/ (3!* 7!) = 120

Hence èP = 120 * (0.5)7 * (0.5)3

P = 0.12



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