so for binomial distribution if I have my n=15 and p=.2
and I have to calculate the probability of exactly 8 fails,
I know I can do something like this,
P(X=8) = P(X<=8) - P(X<=7) = B(8;15,.2) - B(7;15,.2)
in which case,I'm subtracting the two cdf's to obtain the value at X=8,
but can I do something like this
B(8;15,.2) = (15 (.2)^8 (1-.2)^(15-8)
do I have to have to use the cdf's of the binomial random variable or I can also use the simple formula of the binomial theorem?