Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 year ago

What is the probability of of 32 coins landing on heads if 100 coins are flipped?

Update:

Exactly 32

4 Answers

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  • 1 year ago
    Favorite Answer

    I'll assume you want the probability of exactly 32 heads.

    Use the binomial probability formula:

    P(X = k) = C(n,k) * p^k * q^(n-k)

    n : number of trials (100)

    k : number of successes (32)

    p : probability of success (1/2)

    q : probability of failure (1/2)

    P(X = 32) = C(100,32) * (1/2)^32 * (1/2)^68

    = 100!/(32!68!) * (1/2)^100

    = 143012501349174257560226775 / 1267650600228229401496703205376

    ≈ 0.000113

    ≈ 0.0113%

    Answer:

    About 0.0113%

    • Puzzling
      Lv 7
      1 year agoReport

      If that isn't clear, just imagine what would happen if you calculated P(100,32) instead. You'd get a result that was much greater than 1 which isn't possible for a probability.

  • 1 year ago

    .

    Binomial

    P(X = k) = C(n, k) p^k q^(n - k)

    p = probability of a success = ½

    q = probability of a failure = ½

    n = number of tosses = 100

    k = exact number of heads required = 32

    P(X = 32)

    = C(100, 32) (½)³² (½)⁶⁸

    = C(100, 32) (½)¹⁰⁰

    = 100! / (68! 32! ) (½)¹⁰⁰

    = 143012501349174257560226775 / 1267650600228229401496703205376

  • 1 year ago

    pretty likely I'd say. tossing a coin is a 50-50 chance but that's not always the case. out of a large number its possible to get other percentages. I'm pretty sure.

  • 1 year ago

    exactly 32, or at least 32?

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