Tensions between China and Taiwan have escalated in recent weeks, including the airing on China Central Television of a large-scale simulated assault on Taiwan. Some analysts have warned that China may attack Taiwan. One thing that has remained unclear is whether the U.S. would intervene if China attacked Taiwan as the U.S. has had a policy of "strategic ambiguity" that keeps China guessing as to how the U.S. would respond. Let's assume that China's utility if it attacks Taiwan and the U.S. does not intervene is 1500. However, if China attacks and the U.S. intervenes, China's utility is -1200. China's utility from the status quo is 0. The cost of an attack is 200. Assume that China believes that the probability that the U.S. would intervene is 0.40. What will a rational (and risk neutral) China do? Explain why. (Show any calculations in detail; make sure to properly label what it is you are calculating)