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In a recent election for class president, Monika received 7 of the 10 votes and Alfred received 3 of the 10 votes that were cast by the class.
When the machine was counting the votes, it malfunctioned and instead of giving the vote to the correct person,
it gave the vote to each candidate with probability 12 (regardless of whom the vote was cast for).
The probability that the machine gave each student the correct number of votes in the election can be expressed as a/b where a and b are positive, coprime integers.
What is the value of a+b?

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