A sample of 150 subjects is taken from a population which has two subgroups. The subgroup membership of each subject in the sample is known. Each individual is asked a battery of ten questions designed to be independent, in the sense that the answer to any one is not affected by the answer to any other. The subjects answer independently. Data on the results are summarized in the following table:
| GROUP 1 (84 members) | GROUP 2 (66 members) | |||||
| Q | Yes | No | Unc | Yes | No | Unc |
| 1 | 51 | 26 | 7 | 27 | 34 | 5 |
| 2 | 42 | 32 | 10 | 19 | 43 | 4 |
| 3 | 19 | 54 | 11 | 39 | 22 | 5 |
| 4 | 24 | 53 | 7 | 38 | 19 | 9 |
| 5 | 27 | 52 | 5 | 28 | 33 | 5 |
| 6 | 49 | 19 | 16 | 19 | 41 | 6 |
| 7 | 16 | 59 | 9 | 37 | 21 | 8 |
| 8 | 47 | 32 | 5 | 19 | 42 | 5 |
| 9 | 55 | 17 | 12 | 27 | 33 | 6 |
| 10 | 24 | 53 | 7 | 39 | 21 | 6 |
Assume the data represent the general population consisting of these two groups, so that the data may be used to calculate probabilities and conditional probabilities.
Several persons are interviewed. The result of each interview is a “profile” of answers to the questions. The goal is to classify the person in one of the two subgroups
For the following profiles, classify each individual in one of the subgroups
- y, n, y, n, y, u, n, u, y. u
- n, n, u, n, y, y, u, n, n, y
- y, y, n, y, u, u, n, n, y, y
Pfeiffer, Applied Probability, 5.3 Problems on Conditional Independence, exercise 16