Using binomial techniques to solve problems can be useful, especially when one is looking to count the number of successes after a number of trials. Before it can be used, though, it must satisfy these settings:
- Each observation must either be success or failure
- There is a fixed number of observations
- The observations are independant
- The probability of success is the same for each observation
Now, if these conditions are satisfied, the binomial probability can be used. It is stated below:
P(X=k) = ( n ) p^k(1-p)^(n-k)
k
With the binomial coefficient being:
(n) = n!/(k!(n-k)!)
k
And the mean being simply mu = np
and the standard deviation as sigma = sqrt(np(1-p))
