[jasonfish11]

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Two possibilities so they must each have a 1/2 chance of happening, right?

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Yes and that is the biggest problem I have with the formula I have come up with. I think I might have come up with a better solution but still not sure.

As I stated the amount of NYs that will die is grossly overstated. In a real life situation the givens wouldnt be the death counts but instead you would know the amount of evidence you have. I thought that giving the non invasion options both 50/50 chance of happening is wrong. So how about this formula? Lets assume that we have 20% of the evidence says they have WMDs AND are planning on using them on the US. Lets also say we assume 100,000 people will die if we go to war. Can I modify the formula to what is below to find out how many lives must be at risk before invading is correct?

100,000(1) = (.2)X + .8(0)
100,000 = .2X
500,000 = X

Basically if we invade 100% of the time with only 20% of the evidence showing they have WMDs AND are going to use them on the US then there must be more than 500,000 people at risk to warrant invading. Does this seem like a better formula? Since you will have the % evidence as a given, and this differentiates the odds of them using WMDs on American (or what ever country) soil from them not having those WMDs and not using them. This way those 2 outcomes are not equal (because they wouldnt be in real life).

Oh and I think chemical weapons used correctly would kill way more than 82,000 people. For instance you could kill all 250,000 people in the stands of the Daytona 500 with a crop duster.