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  1. #1
    Newbie helloworld101's Avatar
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    Question need help with an expectation question

    hi hi
    am not sure where to begin so all i need is a push in the right direction not the answer. so here's the question

    find the expected number of ones when three ordinary fair dice are thrown.

    i know that E(X) = xP(X=x) but the only thing throwing me off is the three dice so if u can please point me in the right direction
    Thank You so veryyyy much
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    Hello, helloworld101!

    Find the expected number of 1's when three fair dice are thrown.

    We need the probability of getting: one 1, two 1's, three 1's.

    There are: . 6^3 = 216 possible outcomes.


    To get three 1's:
    There is one way to get three 1's.
    . . P(\text{three 1's}) \:=\:\frac{1}{216}


    To get two 1's:
    There are three cases: .[tex]33x, \;3x3,\;x33[/maTH]
    . . And there are 5 choices for the third die.
    There are: . 3\cdot5 \:=\:15 ways to get two 1's.
    . . P(\text{two 1's}) \:=\:\frac{15}{215}


    To get one 1:
    There are three cases: . 3xx,\;x3x,\;xx3
    . . And there are 5^2 choices for the other two dice.
    There are: . 3\cdot25 \:=\:75 ways to get one 1.
    . . P(\text{one 1}) \:=\:\frac{75}{216}


    \text{Expected number of 1's} \;\;=\;\;(3)\left(\frac{1}{216}\right) + (2)\left(\frac{15}{216}\right) + (1)\left(\frac{75}{215}\right) \;\;=\;\;\frac{108}{216} \;\;=\;\;\frac{1}{2}

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  3. #3
    Newbie helloworld101's Avatar
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    much thanks soroban really appriciate it
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    Quote Originally Posted by helloworld101 View Post
    hi hi
    am not sure where to begin so all i need is a push in the right direction not the answer. so here's the question

    find the expected number of ones when three ordinary fair dice are thrown.

    i know that E(X) = xP(X=x) but the only thing throwing me off is the three dice so if u can please point me in the right direction
    Thank You so veryyyy much
    If X is the random variable 'number of ones' then X ~ Binomial(n = 3, p = 1/6) and so E(X) = np = ....
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