88 Probability of winning a war. Before a country enters into a war, a prudent government will assess the cost, utility, and probability of a victory. University of Georgia professor P. L. Sullivan has developed a statistical model for determining the probability of winning a war based on a government’s capabilities and resources ( Journal of Conflict Resolution, Vol. 51, 2007). Now consider the current U.S.–Iraq conflict. One researcher used the model to estimate that the probability of a successful regime change in Iraq was .70 prior to the start of the war. Of course, we now know that the successful regime change was achieved.

However, the model also estimates that given the mission is extended to support a weak Iraq government, the probability of ultimate success is only .26. Assume these probabilities are accurate.

a. Prior to the start of the U.S.–Iraq war, what is the probability that a successful regime change is not achieved?

b. Given that the mission is extended to support a weak Iraq government, what is the probability that a successful regime change is ultimately achieved?

c. Suppose the probability of the United States extending the mission to support a weak Iraq government was .55.

Find the probability that the mission is extended and results in a successful regime change.