Yes, I have a degree in it which is why I am questioning you arbitrary selection of the probability you want to combine.
If you have a degree in statistics you should understand the argument above; anyone can claim anything on here and I do not accept your expertise. Try working it through from first principles.
Two blood dogs each with an average of 80% reliability.
Parallel Case
Dog one alerts giving one reason to believe that there is the possibility of 4 in 5 cases being correct.
Dog two alerts giving one reason to believe that there is a possibility of 4 in 5 cases being correct.
As you are repeating the same test, the second test increases the accuracy and two alerts increase the chance of the dogs being correct.
Serial Case
Dog one alerts giving one reason to believe that there is the possibility of 4 in 5 cases being correct.
Dog two alerts giving one reason to believe that there is a possibility of 4 in 5 cases being correct.
As the two rests are not connected the second test introduces inaccuracy and the accuracy is decreased.