Statistics Question (about invading Iraq)

[jasonfish11]

I recently calculated how much evidence is needed to make invading Iraq the correct decision (death toll wise). I figured there are 4 possible outcomes.
1)Invasion of Iraq kills 82,000 Iraqi civilians whether they have WMDs or not (2 of the 4 outcomes)
3) Iraq does have WMDs and we dont attack. (assuming they would plan to use them in a very populated area like NYC). Population of NYC is 8,200,000.
4) Iraq doesnt have WMDs and we dont attack. No one dies.

I used the entire population of NYC (which is probably more than will actually get killed by a WMD).

Here is the formula I came up with. Please let me know if you see flaws.

X = % of time that invading Iraq will result in a smaller death toll. I took half the population of NY because if we dont attack and they have WMDs 8.2 million people die, but if they dont have WMDs 0 people die. (8.2+0)/2 =4.1 million

82,000x = 4,100,000 (1-X)
82,000x = 4,100,000-4,100,000x
4,182,000x = 4,100,000
X = .98

So if as little as 2.1% of the evidence gathered it would suggest that invading Iraq will have a smaller death toll than not invading and taking the risk. (Both the 82,000 Iraqi civilians and the population of NY were verified by reliable sources online.)

I am wondering if the math is messed up or I made too many assumptions (I think I used a formula usually used to calculate 2 possible out comes when there are actually 4 possible out comes). Because this number seems really low.

Once again I am looking to make sure that math and formula is right. I know that not everyone in NY would die I just took that number to see if the formula worked. If everything is correct I will figure out a more realistic number.

Any help would be appreciated.