Binomial Distribution Calculator

 Number of Trials n= Number of Successes x= Probability of Success p=

All you need to know about Binomial Distributions

is the Binomial Probability formula.

used when the following conditions called "BINS" are fulfilled:
B = Binary (two) outcomes are possible, called Bernoulli trials, ex: Head or Tails, Make or Miss a Free Throw.
I = The events are Independent, ex: getting a head has no impact on the outcome of the next toss.
N = Predetermined Number of trials. ex: we toss a coin 3 times or we take 10 free throws
S = Success probability is constant, ex: P(Head) = 50% or P(make free throw) = 80% = .80

Advanced Information on the Binomial Distribution: Mean=n*p , Standard Deviation =

Sample Binomial Distribution Problem

What is the probability of making exactly 2 of 3 free throws, make probability per free throw is 80% ?
Here, x=2 (the number of successes) , n=3 (the number of trials), p=.8 (success probability)
Plugged into the Binomial Probability formula: $P\left(X=2\right)=3C2*.82*\left(1-.8\right)\left(3-2\right)= 3*.82*.2 = .6*.64 = .384 = 38.4%$
3!/(3-2)!*2! = 3*2*1/(1)(1*2) = 3 which gives the number of ways of making 2 out 3 free throws.
Remember: n!=n*(n-1)*(n-2)*..*3*2*1
Those 3 ways can be listed as MAKE, MAKE, MISS or MAKE, MISS, MAKE or MISS, MAKE, MAKE.
Get it now? Try the above Binomial Distribution Calculator a few more times.

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