# 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."

### 2 Answers

- PuzzlingLv 72 years 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

For example:

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

= 1953125/6718464

≈ 0.2907

Answer:

About 29.1%

- ?Lv 72 years 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

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Yes, say what everything else, but

leaving this part out

Makes the definition lacking.