Suppose that I know the probability of an event occurring by either process 1 or process 2:
process 1, p(event)=1-exp(-ax) process 2, p(event)=1-exp(-by)
With this information, is it possible to calculate the probability of the event occurring by process 1 given that process 2 also occurs?
To be more specific, my process involves a receptor that receives particles either by process 1 or process 2. It models whether or not the receptor is remotely controlled. It assumes that as x (process 1) or y (process 2) increases, there is a greater likelihood of the receptor being brought under control. I now need to know the probability that particles delivered by process 1 control the receptor when process 2 is also delivering particles (and vice versa).
So if there is a 90% chance that process 1 controls the receptor (in the absence of process 2), and an 85% chance that process 2 controls the receptor (in the absence of process 1), would it be possible to determine the probability that process 1 controls the receptor given the process 2's probability in the absence of process 1?
I should also note that I do not know the frequencies, so I could not calculate the relative abundance of particles originating from process 1 and 2.
Thank you kindly