I'm trying to make some predictions about events happening in the next year, and I have a question about the methodology I'm using.
Here's a stylized example of the problem I'm working on:
Alice and Bob are running a marathon for the first time. I'm interested in estimating p(Alice or Bob finish the race) and p(Alice and Bob finish the race), as well as p(Alice finishes the race) and p(Bob finishes the race).
I've done some information gathering on Alice's and Bob's fitness, training schedule and the base rate of first-time entrants finishing marathons. After this research, I believe that p(Alice or Bob finish the race) = 0.75, and that p(Alice and Bob finish the race) = 0.35
To figure out p(Alice finishes the race) and p(Bob finishes the race), I'm considering adding up the two probability estimates I've already made, then divvying up the total probability between the two (based on the information I have about them). So this would look like: 0.75 + 0.35 = 1.10, divvy up as p(Alice) = 0.8 and p(Bob) = 0.3
However, I'm not sure if it is appropriate to add up p(Alice or Bob) and p(Alice and Bob), given that the second event is a subset of the first. Is this an appropriate method for making predictions?
Is there another way I could arrive at predictions for p(Alice) and p(Bob) using the information I have about p(Alice and Bob), p(Alice or Bob), and their backgrounds?