# Michael's walk on the number line

Probability Level 3

An ant starts a random walk on the real number line at $0$. At each step, the ant moves by $+1$ or $-1$ with equal probability. After $6$ moves, the probability that the ant is on a positive number can be expressed as $\dfrac{a}{b},$ where $a$ and $b$ are positive coprime integers. What is the value of $a+b?$

This problem is posed by Michael T.

×