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

###### Question details

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 P_{00} =
P_{11} = 1−α, P_{01} = P_{10} = 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.