Suppose for illustration that there is a 1% chance of bio-x-risk in (the single year) 2030 and a 99% chance of AI-x-risk in 2040 (assuming that we survive past 2030). Then we survive both risks with probability (1-.01)*(1-.99) = .0099. Eliminating the bio-x-risk, we survive with probability 1-.99 = .01.
But if there is no AI risk, eliminating biorisk changes our survival probability from .99 to 1.
So in the two-risk case, P(die) = P(die from bio OR die from AI) = P(bio) + P(AI) - P(bio AND AI) = (using independence) 0.01 + 0.99 − 0.01*0.99 = 1 − 0.0099 = 0.9901. If P(die from bio)=0, then P(die) = P(die from AI) = 0.99.
Suppose for illustration that there is a 1% chance of bio-x-risk in (the single year) 2030 and a 99% chance of AI-x-risk in 2040 (assuming that we survive past 2030). Then we survive both risks with probability (1-.01)*(1-.99) = .0099. Eliminating the bio-x-risk, we survive with probability 1-.99 = .01.
But if there is no AI risk, eliminating biorisk changes our survival probability from .99 to 1.
I see, thanks!
So in the two-risk case, P(die) = P(die from bio OR die from AI) = P(bio) + P(AI) - P(bio AND AI) = (using independence) 0.01 + 0.99 − 0.01*0.99 = 1 − 0.0099 = 0.9901.
If P(die from bio)=0, then P(die) = P(die from AI) = 0.99.
Exactly.