Michael's walk on the number line

An ant starts a random walk on the real number line at 00. At each step, the ant moves by +1+1 or 1-1 with equal probability. After 66 moves, the probability that the ant is on a positive number can be expressed as ab,\dfrac{a}{b}, where aa and bb are positive coprime integers. What is the value of a+b?a+b?

This problem is posed by Michael T.

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