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Math Help - Probability and dice

  1. #1
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    Probability and dice

    Refer to dice that are loaded so that the numbers 2, 4, and 6 are equally likely to appear. 1, 3, and 5 are also equally likely to appear, but 1 is three times as likely as 2 is to appear.

    #1)Two dice are rolled. What is the probability of getting a sum of 6 or doubles given that at least one die shows 2?
    To roll 6: 5/36
    To roll doubles: 6/36
    To have at least one 2: 11/36
    (5/36)/(11/36) = 5/11
    (6/36)/ (11/36) = 6/11

    It this correct?

    #2)Two dice are rolled. What is the probability of getting a sum of 6 or a sum of 8 given that at least one die shows 2?
    To roll 6: 5/36
    To roll 8: 5/36
    To have at least one 2: 11/36
    (5/36)/(11/36) = 5/11
    (5/36)/ (11/36) = 5/11

    It this correct?
    Thank you.
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  2. #2
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    Re: Probability and dice

    You have not used the funny dice.

    p(2) = 1/9
    p(6 total) = 14/81
    p(8 total) = 11/81
    p(doubles) = 5/27
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  3. #3
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    Re: Probability and dice

    how to use the funny dice?
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  4. #4
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    Re: Probability and dice

    Refer to dice that are loaded so that the numbers 2, 4, and 6 are equally likely to appear. 1, 3, and 5 are also equally likely to appear, but 1 is three times as likely as 2 is to appear.
    2, 4, and 6 are equally likely. Give them one point each.

    1, 3, and 5 are equally likely and twice as likely as 2, 4, and 6. Give them two points each.

    That's a total of 1+2+1+2+1+2 = 9 points.

    p(2)=p(4)=p(6) = 1/9
    p(1)=p(3)=p(5) = 2/9

    That is quite a bit different from a fair die, which produces p(1)=p(2)=p(3)=p(4)=p(5)=p(6)=1/6
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  5. #5
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    Re: Probability and dice

    1, 3, and 5 are equally likely and twice as likely as 2, 4, and 6. Why twice as likely as 2, 4, and 6?

    Thanks
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