Final answer:
The question is about calculating the probability of the first defective component appearing at a specific position (seventh) in a sequence of tests, applying the principles of geometric distribution in Mathematics. It highlights the importance of quality control and ethical manufacturing practices.
Step-by-step explanation:
The question deals with the concept of probability and geometric distribution in Mathematics, specifically related to reliability and quality control in a production process. For example, assuming the probability of a defective computer component is 0.02 (2%), and components are randomly selected, the probability that the first defect appears at the seventh component is a particular calculation within the geometric distribution. The symbol X represents the number of components tested until the first defect is found, and it can take on any positive integer value. Using the formula for geometric distribution and possibly a graphing calculator, as suggested in the question, you will find that P(x = 7) is equal to 0.0177. A scenario describing the importance of this calculation is represented by the counter example of an automobile manufacturer who ignored known defects resulting in liability for injuries and deaths.