OR-port $A\cdot B$: its conditional probabilities with zero working probability for each component? Reductio ad absurdum?

Solution 1:

Suppose A works, what is the probability that the system works i.e. $P(T|A)$? Look A has 0% working probability i.e. $P(A)=0$ so what does the phrase "A works" mean here? The term "working" can mean at least two things: $P(A)=1$ or $P(A)>0$. The latter requires thinking probabilities with intervals.

The below threads address the aroused issues so far.

Sub-problems

1. Solved $P(T\cap \neg B)$ if $P(T)=P(A\cup B)$ where $P(A)=0$ and $P(B)=0$?

2. Solved Complement and Negation: $P(A)=0\rightarrow P(\neg A)=1$?

3. Conditional probabilties in the OR-gate $T=A\cdot B$ with zero-probabilities in $A$ and $B$?