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Math Help - Probability Answer Check

  1. #1
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    Probability Answer Check

    If a fair die which six sides is tossed twice what is the probability
    that the lagest face value obtained is twice the smallest face value
    obtained?

    (1/6)^6

    Heres my work:

    Let x = the value of the first roll
    Let y = the value of the second roll

    so if x = 1,2,3,2,4,6
    then y = 2,4,6,1,2,3
    then the pairs are (1,2), (2,1), (4,2), (2,4), (3,6), and (6,3), which is 6 pairs

    the probability of obtaining each value is 1/6
    So I get (1/6)^6
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  2. #2
    Moo
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    Hello,

    Quote Originally Posted by shogunhd View Post
    If a fair die which six sides is tossed twice what is the probability
    that the lagest face value obtained is twice the smallest face value
    obtained?
    Hm, I don't think it's the right reasoning

    Your pairs are OK. Each pair has an equiprobability to be gotten.

    The probability that the first dice yields X (for example 1) is 1/6. The probability that the second dice yields Y (for example 2) is 1/6.
    Hence, the probability of getting the given pair (X,Y) is (1/6)*(1/6)=1/36

    Among the 36 possible pairs, only 6 are the ones you're interested in.

    Therefore, the probability of getting one of the 6 given pairs is 6/36=1/6.

    Do you understand ?
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  3. #3
    Moo
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    So I get (1/6)^6
    What you did here corresponds to the probability of getting one of these pairs every time for the 6 tosses.
    Multiplying probabilities this way corresponds to a repetition of events, independently. It's like tossing 6 times the dice (twice).
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  4. #4
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    Yes, I understand it much better now. Thank you
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