medium Probability
A release-checked medium problem for training Conditional Probability.
An ant starts at the origin in the plane. At each step, with probability $\dfrac{1}{4}$, the ant will move one unit north, south, east, or west. What is the probability that the ant returns to the origin before hitting any point on the boundary of the square with vertices at $(\pm 2, \pm 2)$?
This Probability problem is tagged Conditional Probability. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.
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