What is the binomial probability formula?
I'm trying to answer statistics questions for homework based on a video. I'm confused because the video mentions more than one formula, so I'm unclear about how to answer the question that simply says, "State the binomial probability formula."
- PuzzlingLv 71 year agoFavorite Answer
The binomial probability formula applies when you have n trials where you want k successes of an event that has probability p of success.
P(X = k) = C(n,k) * p^k * q^(n-k)
n : number of trials
k : number of successes
p : probability of success
q : probability of failure
You are rolling a die 10 times. What's the probability of rolling a five exactly 2 times?
n : number of trials (10)
k : number of successes (2)
p : probability of success (1/6)
q : probability of failure (1-p = 5/6)
P(X = 2) = C(10,2) * (1/6)^2 * (5/6)^8
= 10!/(2!8!) * 1/36 * 390625/1679616
= (10*9)/2 * 390625/60466176
= 45 * 390625/60466176
- ?Lv 71 year ago
probability of success in 1 trial is p
probability of k successes in n trials
C(n,k) p^k (1-p)^(n-k)
where C(n,k) is the binomial coefficient