Question 886154
the formula for binomial probability is:
p(x) = nCx * p^x * q^(n-x)
in your problem:
x = 8
n =  11
nCx = 11C8
p^x = .8^8
q^(n-x) = .2^3
your formula becomes:
p(8) = 11C8 * .8^8 * .2^3
that probability becomes:
p(8) = 165 * .8^8 * .2^3 which is equal to .2214592512


nCx is the combination of n things taken x at a time.
the formula for nCx is:
nCx = n! / ((n-x)! * x!)


when n = 11, there are 12 distinct sets of probabilities.
they range from p(0) to p(11).


the sum of all probabilities must be equal to 1 or you did something wrong.


here's a list of all the probabilities for this problem.
as you can see, the total sum of all probabilities is equal to 1.


<img src = "http://theo.x10hosting.com/2014/jul0801.jpg" alt="$$$" </>


here's a link that explains binomial probabilities.


<a href = "http://www.regentsprep.org/Regents/math/algtrig/ATS7/BLesson.htm" target = "_blank">http://www.regentsprep.org/Regents/math/algtrig/ATS7/BLesson.htm</a>