Question 1118171
the binomial probability formula is:


p(x) = c(n,x) * p^x * q^(n-x)


c(n,x) is the number of ways you can get a set of x elements out of a set of n elements when order of the elements within each set of x elements is not important.


that formula is c(n,x) = n! / (x! * (n-x)!).


p = .24
q = 1 - .24 = .76
n = 4
x = 0 to 4



p(x = 2) would be c(4,2) * .24^2 * .76^2 = 0.19961856
p(x = 3) would be c(4,2) * .24^3 * .76^1 = 0.04202496
p(x >= 2) would be p(x = 2) + p(x = 3) + p(x = 4) = 0.24496128
p(x < 3) would be p(x = 0) + p(x = 1) + p(x = 2) = 0.95465728


the complete analysis is shown in the following spreadsheet.


<img src = "http://theo.x10hosting.com/2018/060502.jpg" alt="$$$" >


the sum of all probabilities is equal to 1, as it should be.