1. If A1 is independent of A2, P (A) | A2) = P (A2). Exercises 15–20. The Human Resources division classifies employees of the firm into one of three categories: administrative, clerical, or management. Suppose we choose an employee at random. Define the events
A = {administrative},
C = {clerical},
M = {management}
Event A occurs, for example, if the randomly chosen employee is an administrator. Event S occurs if the randomly chosen employee (from any category) makes more than +120,000 annually.
2. P (A and C) = P (A) × P (C).
3. If event A is independent of event S, then P(A | S) = P(S | A).
4. Independence of S with each of A, C, and M implies that an equal proportion of employees within these categories makes above +120,000 annually.
5. If 20% of the employees who make more than +120,000 annually are in management and 40% of the employees who make more than +120,000 annually are administrative, then P1M2 6 P(A).
6. If we pick an employee at random from the clerical employees, then P(S | C) is the probability that this employee makes more than +120,000 annually.
7. If 75% of employees who work in management make more than +120,000 annually but only 30% of employees in the firm as a whole make more than +120,000 annually, then the events S and M are dependent.