medium Probability
A release-checked medium problem for training Combinatorics, Conditional Probability.
You have a $5 \times 5$ checkerboard. You randomly place a checker in the center $3 \times 3$ grid. The checkers can move in two equally random ways: up to the left, and up to the right. If the checker is on the boundary, then it can only make valid moves. What is the probability that the checker ends up in the top-left or top-right corner?
This Probability problem is tagged Combinatorics, 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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