easy Probability

Below Diagonal

A release-checked easy problem for training Law of Total Probability, Conditional Probability.

Question

A square has vertices at $(0,0), (0,4), (4,4),$ and $(4,0)$. A bug starts at $(3,2)$ on the interior of the square. The bug moves in each of the $4$ cardinal directions with equal probability at each step. The bug stop when it crashes into one of the sides of the square. Find the probability that the bug ends up crashing into the square on a vertical side.

Practice focus

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.