Proof: A measure of how much alcohol (ethanol) is contained in an alcoholic beverage. The term was originally used in the United Kingdom and was defined as 7/4 times the alcohol by volume (ABV). The UK now uses the ABV standard instead of alcohol proof. In the United States, alcoholic proof is defined as twice the percentage of ABV.
This is proof that proof has been proven. No pudding need for putting this proof into because the proof is actually in the proof.
Conditional probabilities, sir. If the dice reader says it is a six then what is the probability that the dice rolled a six?
If your reader is always faithful and is displaying 6 then the outcome of the 1-6 probability came in as a 6
If I told you that my dice reader is designed to never display the correct result ...
If your device is a faithful liar then when it says 6 you are assured the roll was not 6. But the roll itself was a 1-6 chance. If the roll landed on 6 then your faithful liar would display a different number.
Your wolf detector has only a 1/365 chance of being right each - and - every - day, regardless of how many times you try.
Exactly. Where did this number come from? Did you derive this number from the number of false positives?
The 1/365 accuracy rate is indeed established by the number of false positives experienced. Once established that rate, unless you change the detector, remains. I agree.
If so, then you agree that the number of false positives do effect the probability that the next alarm will be correct.
There appears to be a vernacular problem here. I'm thinking you are looking at one situation and I am seeing another.
Are you saying that after 19 days of false positives you can tentatively say the next day has a 1-20 probability of being right? Then at 39 days of constant false positives you are now saying that the next day has a 1-40 chance of being correct?
If so then this is all basakwards. You cannot say anything about the probabilities until you hit on a true positive.
I will grant you that on the 39th day you can say that the next day has "at least a 1-40 chance" with the caveat that it may be considerably more than 1-40 and is thus unknown. You have only placed a lower bound.
But can you not see that as the number of false reports goes up, our confidence in the reports goes down?