Practice Test #1: SM230 Spring '97

Questions:

1. In the Gulf War some troops were on duty near the destruction of chemical weapons. The data in this problem is fictional, but typical of newspaper reports. A study of troops on duty within 25 km of the destruction site have a probability of 0.35 of having certain symptoms. A study troops stationed more that 25 km from the destruction site have a probability of 0.10 of having these same symptoms. If 60% of a certain Army division was on duty within 25 km, and the others were not, what is the probability that a member of this division with exhibit these symptoms?
2. With the same assumptions of problem #1, if a member of this division exhibits these symptoms, what is the probability that this member was stationed within 25 km of the site?
3. Again with the same assumptions as problem #1, what is the probability that a member of this division was stationed within 25 km of this site and exhibited these symptoms?
4. Again with the same assumptions as problem #1, what is the probability that a member of this division was stationed within 25 km of this site or exhibited these symptoms?
5. How are the events of having symptoms and being on duty within 25 km correlated? Explain.
6. A ship sank off the coast of Maryland during a storm in 1835. There are some historical records that suggest where it sank, but are not accurate enough to determine where the wreck is. Assume there is a probability of 0.37 that the wreck is in the shallow coastal water; a probability of 0.18 that it is on the slope joining the deep ocean from the coastal water; and the remaining probability is that the wreck is in the deep ocean waters. The shallow waters are easiest to search, but not all that easy. There is a probability of 0.25 that the wreck will be found this summer, if it is in the shallow coastal waters and those waters are searched; 0.08 probability, if it is on the slope; and 0.15, if it is in the deep ocean waters. If all three areas are searched what is the probability that the wreck is found this summer?
7. Continuing #6, if you were to search one of these regions next summer, which one would you search?
8. Continuing #6, if you search only the deep ocean waters next summer and the wreck is still not found, what is the probability that the wreck is in the shallow coastal waters?