Question

for n repeated independent trials, with constant probability of success p for all trials, find the probability of exactly x succes n=20,p=1/8, x=2
I know the answer but I do not know how to get to that. Answer is 0.268 should I reduce fraction?

Answer 1

To determine probability of binomial distribution for success (x=2) use the following ...
[n choose x] * p ^x * (1-p) ^ (n-x) where
for the first part ...
[n choose x] =
n! divided by [x! * (n-x!)]
so we have 20! / (2! * 18!)
= 20 * 19 / 2 = 190
the second part we have
p ^ x = (1/8) ^ 2 = 1/64 = 0.015625
the third part we have
(1-p) ^ (n-x) = (7/8) ^ 18 = 0.090395
and finally 190 * 0.015625 * 0.090395 =
0.26836