It does, in fact, take her only a minute.

P(hypothesis 1 ◁ observation 1) * P(observation 1) + P(hypothesis 1) ◁ ~ observation 1) * P(~ observation 1) = P(hypothesis 1).

If you add up how much you'd believe in something, given a piece of evidence, times your chance of seeing that evidence, with how much you'd believe something, if you saw not that evidence, times the chance of seeing not that evidence, it's just the same probability you started with.  You can end up convinced of things, you just can't expect to be convinced of them.  Any time you go look for something, that you're hoping will convince you of something, there's a counterbalancing chance you won't find it and then the math requires you to end up believing less.  On net it all balances out.

"I've got #6, no time to explain it though, tell me about #7, not in math I have the math now just what it does it mean."

It does, in fact, take her only a minute.

P(hypothesis 1 ◁ observation 1) * P(observation 1) + P(hypothesis 1 ◁ ~ observation 1) * P(~ observation 1) = P(hypothesis 1).

If you add up how much you'd believe in something, given a piece of evidence, times your chance of seeing that evidence, with how much you'd believe something, if you saw not that evidence, times the chance of seeing not that evidence, it's just the same probability you started with.  You can end up convinced of things, you just can't expect to be convinced of them.  Any time you go look for something, that you're hoping will convince you of something, there's a counterbalancing chance you won't find it and then the math requires you to end up believing less.  On net it all balances out.

"I've got #6, no time to explain it though, tell me about #7, not in math I have the math now just what it does it mean."

It does, in fact, take her only a minute.

(P(hypothesis1 ◁ observation1) * P(observation1)) + (P(hypothesis1 ◁ ~observation1) * P(~observation1)) = P(hypothesis1).

If you add up how much you'd believe in something, given a piece of evidence, times your chance of seeing that evidence, with how much you'd believe something, if you saw not that evidence, times the chance of seeing not that evidence, it's just the same probability you started with.  You can end up convinced of things, you just can't expect to be convinced of them.  Any time you go look for something, that you're hoping will convince you of something, there's a counterbalancing chance you won't find it and then the math requires you to end up believing less.  On net it all balances out.

"I've got #6, no time to explain it though, tell me about #7, not in math I have the math now just what it does it mean."