# Voter Fraud

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 $$\frac{1}{2}$$ (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 $$\frac{a}{b}$$ where $$a$$ and $$b$$ are positive, coprime integers. What is the value of $$a + b$$?

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