I don’t post here much (yet), and normally I feel fairly confident in my understanding of basic probability...
But I’m slightly lost here. “if the Sidewalk is Slippery then it is probably Wet and this can be explained by either the Sprinkler or the Rain but probably not both, i.e. if we’re told that it’s Raining we conclude that it’s less likely that the Sprinkler was on.” This sentence seems… Wrong. If we’re told that it’s Raining, we conclude that the chances of Sprinkler is… Exactly the same as it was before we learned that the sidewalk was wet.
This seems especially clear when there was an alarm, and we learn there was a burglar—p(B|A) = .9, so shouldn’t our current p(E) go up to 0.1 * p(E|A) + p(E|~A)? Burglars burgling doesn’t reduce the chance of earthquakes… Adding an alarm shouldn’t change that.
What am I missing?
Ah, okay. This makes sense to me, but I found the wording rather confusing. I’ll have to warn people I suggest this article to, I suppose.
Thank you kindly!