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    Simple Probability Question




    OK, so I am wondering about something and am not good with probability, but maybe someone here has the answer

    You have a die with only 4 sides, with the numbers 1-4 written on the sides. You roll the die 5 times. What is the probability of the number 2 showing up:

    Once?
    Twice?
    Three times?
    Four times?
    All five times?

    Thanks in advance!
    Last edited by jp023; 06-25-2014 at 10:44 AM.

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    Re: Simple Probability Question

    Check out the Binomial distribution.

    The probability of a success on one throw is P(Throw a 2) = 1/4, assuming the die is fair.

    P(one 2 in 5 throws) = 5C1 (1/4)^1 (3/4)^4 = 405/1024 (≈ 0.396)
    P(two 2’s in 5 throws) = 5C2 (1/4)^2 (3/4)^3 = 270/1024 (≈ 0.264)
    P(three 2’s in 5 throws) = 5C3 (1/4)^3 (3/4)^2 = 90/1024 (≈ 0.088)
    P(four 2’s in 5 throws) = 5C4 (1/4)^4 (3/4)^1 = 15/1024 (≈ 0.015)
    P(five 2’s in 5 throws) = 5C5 (1/4)^5 (3/4)^0 = 1/1024 (≈ 0.001)

    Can you see the pattern?

    Note that the sum of the above probabilities is 781/1024 (≈ 0.763), which is the probability of throwing at least one 2 in five throws. If we apply the same formula to determine what the probability is of getting zero 2’s in five throws, we obtain:

    P(zero 2’s in 5 throws) = 5C0 (1/4)^0 (3/4)^5 = 243/1024 (≈ 0.237)

    Now 781/104 + 243/1024 = 1024/1024 = 1. This is not a coincidence.

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    jp023 (06-25-2014)

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    Re: Simple Probability Question


    you rock. thank you!

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