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Math

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Sam rolls a standard die, and then Ruth rolls the same die. The probability that Ruth's number is higher than Sam's can be written as a/b where a and b have no common factors greater than 1. Find a.

  • Math -

    There are six numbers, 36 boxes below
    * 1 2 3 4 5 6 Sam
    1
    2 *
    3 * *
    4 * * *
    5 * * * *
    6 * * * * *
    Ruth
    (5 + 4 + 3 + 2 +1)/36 = 15/36 = 5/12

  • Math -

    5. The probability that both Sam’s
    and Ruth’s roll produce the same result
    is 1/6. The likelihood that Ruth has the
    higher number is the same as the likelihood that Sam has the higher number.
    Thus, we divide the remaining 5/6 in
    half to get 5/12; the numerator is 5.

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