An ant on a triangle

Probability Level 4

An ant is on the vertex of a triangle. It can move 'left' with probability of 12\frac{1}{2} and 'right' with probability of 12\frac{1}{2}. Note that, the meaning of "moving left or right" is on the corresponding triangle's sides. The expected number of moves till it first reaches its starting point is ab{\dfrac{a}{b}}, where a{a} and b{b} are positive coprime integers. Calculate a+b{a+b}.

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