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Thread: Probability of throwing "too many" 1's

  1. #1
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    Probability of throwing "too many" 1's

    Hello

    Suppose I have a 6-sided, honest dice. I throw this dice 18 times and get the value 1 4 times.
    How do I calculate the probability of this happening?
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  2. #2
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    Re: Probability of throwing "too many" 1's

    The number of 1's rolled out of 18 rolls is binomially distributed with parameters $n=18,~p=\dfrac 1 6$

    $P[4] = \dbinom{18}{4}\left(\dfrac 1 6\right)^4 \left(\dfrac 5 6\right)^{18-4} = \dfrac{518798828125}{2821109907456} \approx 0.1839$
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