easy Probability
A release-checked easy problem for training Law of Total Probability, Conditional Probability.
A tiny cat is sitting on the top left corner of an $8 \times 8$ chess board. At each turn, the tiny cat uniformly at random chooses an adjacent square to move to (including diagonally). What is the probability that the cat is back in the top left corner after $2$ moves?
This Probability problem is tagged Law of Total Probability, 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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