Table of contents | |
Introduction | |
Binomial Distribution Criteria | |
Bernoulli Trials | |
Binomial Distribution – Formula | |
Mean and Variance of a Binomial Distribution | |
Solved Example |
It is also being used in social science statistics as elementary units for the models of dual outcome variables. You can take the examples of election polls; whether the party ‘A’ will win or the party ‘B’ will win in the upcoming election. Whether by implementing a certain policy the government will get the expected results within a specific period or not.
There are three different criteria of binomial distributions described below which the binomial distributions need to fulfil.
Whenever you are doing an experiment you need to find out whether this distribution is binomial or not, once you figure that out then you can apply the binomial formula and can count the probability.
Here are the steps.
Find out the ‘n’ from the problem. Here n = 9
Identify ‘X’. X = the number you are asked to search the probability for is 6.
(Divide the formula then it become easy to get the solution) solve the first part of the formula: – n! / (n-X)! X!
Now add the variables = 9! (9-6)!*6! = 84. And keep it aside for further uses.
Now find out the P and Q. P= the probable chances of success and Q= the possibility of failure. As mentioned in the above question p = 80% or 0.8 so, the probability of failure = 1-0.8 = 0.2 (20%)
Now let’s do the second part of the formula. Px = 0.86= 0.262144
Q(n-x) = 0.2(9-6) = 0.23 = 0.008 (third part of the formula)
Multiply the answer you get from step 3, 5, 6 together
8 × 0.262144 × 0.008 = 0.176
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