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Red Die White Die - Answer

There are 6 x 6 possible red die / white die fractions. The value of the denominator can be a number 1 through 6. For each of these, the numerator can also be a number 1 through 6.

The sum of the integers 1 through 6 is 21. Therefore, the sum of all possible fractions is 21(1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6) = 1,029/20.

The expected value is then 1,029/720 = 343/240 = 1.429167