what is the probability that exactly 5 out of 15 test subjects fail a test
in a 94% success rate?
Since the problem is about failures, and binomial probability is about
successes, we have two choices. Either consider a failure to be a success,
which sounds contradictory, or to rewrite the problem in terms of successes.
I will choose to rewrite the problem in terms of successes, using the fact
that saying "exactly 5 out of 15 fail" is the same as saying "exactly 10 out of
15 succeed". So we rewrite the problem as:
what is the probability that exactly 10 out of 15 test subjects succeed in
passing a test in a 94% success rate?
The probability of getting exactly x successes out of n trials where the
probability of 1 success in 1 trial is p, is given by the formula
C(n,x)pxqn-x where q = 1 - p
Here n = 15, x = 10, p = .94, q = 1-.94 = .06
C(15,10)(.94)10(.06)15-10
3003(.94)10(.06)5 = .0012577378
Edwin
