Final answer:
The probability of defects in a lot remains the same due to the assumption that defects are randomly spread throughout. Examples given include inspecting DVD players and testing computer components, employing principles like random sampling, geometric distribution, and the law of large numbers. Correct option is b. Defects are randomly spread throughout.
Step-by-step explanation:
The student's question concerns the concept that, statistically, the probability of defects in a lot remains the same. The correct assumption that supports this statement is 'b. Defects are randomly spread throughout'. This means that defects occur independently and do not influence each other's occurrence, adhering to the rules of probability such as the product rule and the law of large numbers. In terms of quality control and probability, this can be illustrated through random sampling in scenarios like inspecting a batch of DVD players for defects or testing computer components until a defect is found.
An example provided, referenced as 'Example 4.22', illustrates a scenario where an inspector wants to calculate the probability of finding at most two defective DVD players in a sample of 12, knowing there are 10 defective players among 100. This scenario also reflects the fixed number of trials, the independent nature of each trial, and the fact that the probability of finding a defective item does not change with each trial, according to geometric distribution and the law of large numbers.
In 'Example 4.19', we look at the probability of the first defect occurring at a certain point in a sequence of trials. In this case, the fixed probability of 0.02 applies to each individual component tested, and the geometric distribution is again utilized to calculate the likelihood of discovering the first defective component on the seventh test.