Prior to initiating the 2003 war with Iraq, U.S. president George W. Bush had to assess the probability that Iraq had weapons of mass destruction. Bush's relative payoffs from invading arguably depended upon the state of the world.

	Weapons (S1)	No Weapons (S2)
Attack (A1)	Iraqi invasion provides proof of US claims and averts threat (C1)	Iraqi invasion fails to provide evidence of US claims, but Hussein is removed. (C3)
Do not Attack (A2)	Iraq continues to build stockpile of weapons and continues as an active member of Bush's "Axis of Evil" (C4)	No war needed, but troops have nothing to do in desert. (C2)

Assume that for Bush U(C₁) = 1, U(C₂) = .3, U(C₃) = .1 and U(C₄) = 0

1. How probable must it be that Iraq has weapons of mass destruction for Bush to prefer an attack?
2. How does this probability change as U(C₂) gets higher or lower?