I'm trying to solve this exercise but i don't know where to start. The exercise is:
I have two types of signals with codes $111$ or $000$ with probabilities of $0.65$ and $0.35$ respectively. These signals are distorted by noise, which provocates that a $1$ (sent) can be receipt as $0$ with a probability of $0.2$ and the converse with $0.8$. Suppose that the symbols suffers these noises independently.
Which is the probability of get in the output we receive the signals $111$, $000$ and $010$ ?
$111$ sent and received correctly $(0.65\cdot0.80^3)$
$000$ sent and received as $111$ $(0.35\cdot0.20^3)$
P(111) received $(0.65\cdot0.80^3) + (0.35\cdot0.20^3)$
$111$ sent and received as 010 $=(0.65\cdot0.80\cdot 0.2^2)$
$000$ sent and received as 010 $=(0.35\cdot0.80^2\cdot 0.2)$
etc.