\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
A laboratory rat is placed in a maze with two rooms, Room A and Room B. The probabilistic graph below shows the transition probabilities between rooms every minute. Let \(X_n\) be the random variable representing the room occupied by the rat at minute \(n\).
  1. If the rat is in Room A, what is the probability \(P(X_{n+1}=B \mid X_n=A)\)?
  2. If the rat is in Room B, what is the probability \(P(X_{n+1}=B \mid X_n=B)\)?
  3. Verify that for each node, the sum of the weights of the outgoing edges is 1.

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