“One word for probability one is “certainty” and a word for probability zero is “impossible”.”
I think you should be cautious about using these words like this, at least if you might be talking about uncountable probability spaces. Using your definitions it is certain that (say) a normally distributed variable takes a value in the real numbers but impossible for it to take any such value.
I hope this isn’t unfairly pedantic to point out. I can see that one could argue that for decision making in the real world you only assign probabilities to finitely many outcomes.
“One word for probability one is “certainty” and a word for probability zero is “impossible”.” I think you should be cautious about using these words like this, at least if you might be talking about uncountable probability spaces. Using your definitions it is certain that (say) a normally distributed variable takes a value in the real numbers but impossible for it to take any such value.
I hope this isn’t unfairly pedantic to point out. I can see that one could argue that for decision making in the real world you only assign probabilities to finitely many outcomes.