Probability of a signal gets transmitted

Pa + Pb - PaPb

You have two paths A and B, so the probability is additive BUT, you are overstating the probability because A and B overlap and you can't have both A and B successful so you have to remove the overlap. Consider two coins. What is the probability one will be heads if you flip them. Each coin has a 50% chance, so if you add them together, you get 100% which is clearly wrong. You have to subtract out the overlap, the region where both came up heads, so you get 50% + 50% - 25% = 75%, the correct answer.

I agree with Engineer's result, but my reasoning would be different. I would start by observing that the transmission succeeds unless it fails on both paths. The probability of failing on both paths is straightforward to calculate:

P_fail = (1-Pa)*(1-Pb) = 1 - Pa - Pb + Pa*Pb .

Now that we know the probability of failure, let's calculate the probability of success:

P_success = 1 - P_fail
= 1 - (1 - Pa - Pb + Pa*Pb)
= Pa + Pb - Pa*Pb

QED.