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? |

Well, duh.

Is this too pedantic?