Question: consider the problem of sending a binary message 0 or...

Consider the problem of sending a binary message, 0 or 1, via a signal channel consisting of several stages where transmission through each stage is subject to a fixed probability of error, α ∈ (0,1). Assume X0 = 0 is the original signal that is sent and let Xn, be the signal received at the nth stage. Assume {X_n} is a Markov chain with transition probabilities P₀₀ = P₁₁ = 1−α, P₀₁ = P₁₀ = α

Determine the probability that the first time an incorrect signal is received is at stage n = 3.

Note: you need to express this as an appropriate joint event and compute its probability.