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Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 years ago

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."

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  • 2 years ago
    Favorite 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%

    • ...Show all comments
    • Alan
      Lv 7
      2 years agoReport

      Yes, say what everything else, but
      leaving this part out
      Makes the definition lacking.

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  • ?
    Lv 7
    2 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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