Name_____________________

W. C. Mylander SM230 Hour Exam #1

5 February 1997 (A closed book Exam. Show work and give the

final answers correct to 3 decimal places.)

(30 points)

1. At a military school 52% of the faculty are civilian and 28% of the faculty drive foreign cars. A survey of the stickers on cars in the lot indicates that 40% of the foreign cars are driven by the military faculty.

a. Draw the box Venn diagram for this problem.

b. What fraction of the faculty are military and drive domestic cars?

  1. If the country of the maker of cars is independent of the status of faculty members what is the percentage of cars that are foreign and driven by military faculty?
  2. What is the correlation (if any) between being a military faculty member and drivers of cars made by a foreign company? What is the correlation (if any) between being a military faculty member and drivers of cars made by a domestic company?








(15 points)

2. In translating the following statements into the mathematical expression P[A|B] identify the sets A and B.

  1. If it's raining, it is probably Saturday.
  2. Blacks are over-represented in the prison population.
  3. The more you study the higher your grade is likely to be.

(18 points)

  1. The following probabilities are known for two events defined involving the outcome of the same chance situation. P[A]=3/10, P[B|A]=1/3, and P[B|Ac]=3/7.
    1. Draw the box Venn diagram for this situation.
    2. Compute P[Ac].
    3. Compute P[AB]
    4. Compute P[A|Bc]

(5 points)

4. The set A is the days Sunday, Wednesday, Thursday and Friday and the set B is the days of the week this section of SM230 normally meets. What is membership of the set ABc?



(32 points)

5. A submarine is lost on the continental shelf, the bottom is muddy and detection will be very difficult. The region known to contain the lost sub has been subdivided into subregions as shown below with the probabilities the sub is in each subregion shown by the bold faced numbers in the cells. In a half day of search of a cell the probability of detecting the sub given it is in the subregion being searched is .4.

1) .182) .18 3) .10
4) .165) .21 6) .17

The western subregions of the region (cells 1) and 4) ) are searched in sequence in a continuous search on the first day.

  1. Construct the box Venn diagram used to analyse the first day of search.
  2. What is the probability this day of search will result in a detection?
  3. If this first day of search is unsuccessful what is the probability the sub is cell 5?
  4. If the probability of detection in cells 1), 2), and 3) is .6 in a half day of search and in cells 4), 5) , and 6) is .3, which cell should have been searched first?