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The Get The Last Word In Thread

AmishTickler said:
Please DO. 😀
Click to expand...
I will. I don't like to be asked to prove anything here. The last time that I did post a proof here, I got all kinds of shit for it in the P&R FORUM. 😀
This was the proof that I posted:
I am coming out of self-imposed exile from the P&R Forum to start this
thread. I don't intend to make posts in any other thread or to start any
other threads any time soon.

Title:
Theorem for a cold, snowy winter

Notation:
Where E is any event in a sample space, let P(E) represnt the
probability of E; let ~E represent the complementary event, that
E does not happen; and let P(~E) represent the probability of ~E.

Where E and F are events in a sample space and where F is possible,
let P(E|F) represent the conditional probabilty of E, given that F has
already happened.

THEOREM
Let A and B be events in a sample space. Let B be possible but not certain.
Then:
If P(A|B) > P(A), then P(A|~B) < P(A).

Statement of the theorem in words: If B happening makes A more probable,
then B not happening makes A less probable.

Proof of the theorem:

Let P(A) = a and P(B) = b. Note P(~B) = 1-b.
Let P(A and B) = x.

Recall that P(A|B) = x/b and we are given that this is greater than a.
Therefore, x > ab
Let d = x-ab. We know that d>0.

Note that P(A and ~B) = a-x = a-ab-d

Now note that P(A|~B) = P(A and ~B)/P(~B) = (a-ab-d)/(1-b)
= (a-ab)/(1-b) - d/(1-b) = a - d/(1-b) < a = P(A)
where the inequality is true because both d>0 and 1-b>0 (because B is not
certain).

quod erat demonstrandum


Why is this in the Politics & Relgion Forum?

Let A be "Anthropogenic global warming is a real problem."
Let B be "This winter is warmer than normal."

Anybody who can't see the point is innumerate.
Click to expand...
 
milagros317 said:
We have that in common here on the TMF, my friend.
At work, I don't mind being asked for a proof in class because I am paid, among other things, to explain PROOFS. 😀
Click to expand...

I didn't think you were going to show up here this EVENING. 😀
 
AmishTickler said:
I will most likely be watching the Flyers first round playoff game vs the Washington CAPITALS. 😀
Click to expand...
Yes, I know that it is NHL playoff time because fans of one of the local teams (the Rangers) are walking the streets in team JERSEYS. 😛
 
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