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chodadog · 12-17-2004, 02:56 PM

RECAP!

In all this back and forth shit, everything has been kind of spread out. I won the ebay auction i was waiting for so i'm going to make one last post before i fuck off to bed for you guys to read and think about.

3 boxes. 1 has a prize in it.

Initially, you have a 1 in 3 chance of picking the correct box.

An incorrect box is then removed, leaving you with 2 boxes. One is the prize. The other is not. Two boxes. 50 percent chance. That makes it 1 in 2. You're then offered the ability to switch. If you choose not to switch, you're left with a 1 in 2 chance. If you elect to switch, you now have a 2 in 4 chance, which is the same as a 1 in 2 chance.

Let me explain.

At first, there are 3 boxes and a total of 3 outcomes each with a 33.3333% chance of occuring.
A box is then removed. The 3 becomes 100% irrelevant. You now have two boxes and a total of 2 possible outcomes. These outcomes each now have a 50% chance of occurring.
You are then offered a switch. This gives each of the 2 existing possible outcomes another possible outcome each, leaving you with a total of 4 possible outcomes. 2 of them will win if you elect to stay. 2 of them will win if you elect to switch giving you a 2 out of 4 chance, i.e., 1 in 2 chance of choosing the correct box. Illustrated below:

Outcome Number 1: If A is right
then the host reveals B
and switching does NOT pay off
OR
Outcome Number 2: the host reveals C
and switching does NOT pay off

Outcome Number 3: If B is right
then the host reveals C
and switching does pay off

Outcome Number 4: If C is right
then the host reveals B
and switching does pay off

2 out of 4 = 1 out of 2.

That should explain it enough.

But to further prove just how irrelevant the third box is, ponder this. You're given 2 boxes. You get to choose one. Then after making your choice, you get told you can change your mind. There are 4 possible outcomes.

The third box is absolutely irrelevant. It serves no purpose whatsoever. This is further illustrated by the fact that NO MATTER WHAT YOU DO, an incorrect box will always be taken away and you'll be left with one right, and one wrong. No matter fucking what! Can't you see how that completely negates the third box?

Anyways. I'm off. Bedtime for me.

12-17-2004, 02:56 PM
chodadog Confirmed User Join Date: Apr 2002 Posts: 9,736	RECAP! In all this back and forth shit, everything has been kind of spread out. I won the ebay auction i was waiting for so i'm going to make one last post before i fuck off to bed for you guys to read and think about. 3 boxes. 1 has a prize in it. Initially, you have a 1 in 3 chance of picking the correct box. An incorrect box is then removed, leaving you with 2 boxes. One is the prize. The other is not. Two boxes. 50 percent chance. That makes it 1 in 2. You're then offered the ability to switch. If you choose not to switch, you're left with a 1 in 2 chance. If you elect to switch, you now have a 2 in 4 chance, which is the same as a 1 in 2 chance. Let me explain. At first, there are 3 boxes and a total of 3 outcomes each with a 33.3333% chance of occuring. A box is then removed. The 3 becomes 100% irrelevant. You now have two boxes and a total of 2 possible outcomes. These outcomes each now have a 50% chance of occurring. You are then offered a switch. This gives each of the 2 existing possible outcomes another possible outcome each, leaving you with a total of 4 possible outcomes. 2 of them will win if you elect to stay. 2 of them will win if you elect to switch giving you a 2 out of 4 chance, i.e., 1 in 2 chance of choosing the correct box. Illustrated below: Outcome Number 1: If A is right then the host reveals B and switching does NOT pay off OR Outcome Number 2: the host reveals C and switching does NOT pay off Outcome Number 3: If B is right then the host reveals C and switching does pay off Outcome Number 4: If C is right then the host reveals B and switching does pay off 2 out of 4 = 1 out of 2. That should explain it enough. But to further prove just how irrelevant the third box is, ponder this. You're given 2 boxes. You get to choose one. Then after making your choice, you get told you can change your mind. There are 4 possible outcomes. The third box is absolutely irrelevant. It serves no purpose whatsoever. This is further illustrated by the fact that NO MATTER WHAT YOU DO, an incorrect box will always be taken away and you'll be left with one right, and one wrong. No matter fucking what! Can't you see how that completely negates the third box? Anyways. I'm off. Bedtime for me. __________________ 26 + 6 = 1