SWAT Team Decision Exercise

Background: You are an Intelligence Officer supporting a Special Weapons and Tactics (SWAT) team planning to assault a terrorist hide-out and rescue several kidnapped citizens. Your Commander has asked you to calculate the probability that the kidnapped citizens will be released as a result of the assault. Construct a probability tree analysis considering the following:
1. The success or failure of the SWAT team reaching the terrorist hideout.
2. An attempt by the terrorists (yes or no) to booby-trap the kidnapped citizens with explosives.
3. The killing of the kidnapped citizens (none, some, all) during the rescue attempt.
You have carefully analyzed the situation and determined there is a 0.6 probability of the SWAT team reaching the terrorist hideout and a 0.4 probability that the kidnapped citizens will be booby-trapped with explosives. If the kidnapped citizens are booby trapped, there is a 0.5 probability that all will be killed during the assault, a 0.3 probability that some will be killed, and a 0.2 probability that none will be killed. If the kidnapped citizens are not booby-trapped, there is a 0.4 probability that none will be killed, a 0.4 probability that some will be killed, and a 0.2 probability that all will be killed.

Calculate the total probability that all of the kidnapped citizens will be rescued. You’re your work by illustrating (i.e. draw a picture either by hand or using a program like PowerPoint, Word or Visio) each branch of the decision tree for all possibilities and subsequent calculations. Then describe your results in narrative form. (10 points)