Expressing probability of bit error

1. May 6, 2013

Evo8

1. The problem statement, all variables and given/known data
I need to the probability of bit error in terms of integrals and terms of conditional probabilities.

Its a bipolar system using threshold detection
https://www.physicsforums.com/attachment.php?attachmentid=58542&stc=1&d=1367888259

2. Relevant equations
probability of bit error → $P_e=Q(\rho)$
$\rho = \frac{A_p}{\sigma_n}$

3. The attempt at a solution
Im not sure I understand whats going on in the figure for this question. I would think that the bit error would be the shaded regions correct? I might be able to figure something out for expressing it in terms of conditional probability but I don't think it would be 100% correct. On top of that I have no idea how to express them in terms of integrals.

Im kind of guessing here but would it be something like $$P_e=p(r|-a) \ + \ p(r|a)$$

Im thinking no...

Any help or hints are greatly appreciated!

2. May 6, 2013

rcgldr

I've normally seen error rates based on bit error rate in this fashion:

bit error rate = p
probability of a good bit = 1 - p
probability of a good byte (8 good bits) = (1-p)^8