Final answer:
The question involves finding probabilities related to defective units using binomial or geometric distributions. Specific probabilities such as for no defects, all defects, or at least one non-defective unit are to be calculated using the provided values for the number of units and the probability of a defect.
Step-by-step explanation:
The question pertains to finding the probability of certain events related to a hypothetical situation involving defective units in a quality control process. This is a problem of probability and can be approached using concepts such as the binomial distribution for non-defective and defective units or the geometric distribution if we are considering the probability of finding the first defective unit after a series of tests.
For instance, if the random variable X defines the number of defective units out of a certain number of units tested, the probability of receiving no defective units (a), all defective units (b), and at least one good unit (c) can be found by applying the respective probability distribution formulas. This mostly likely involves the use of a binomial distribution, where for a given number of trials n and a probability of success (or in this case, defect) p, one can calculate the different scenarios using this distribution's properties.
While the exact calculations depend on additional information that is not provided, such as the number of units being tested or the probability of a unit being defective, the general approach would be:
- For no defective units, use the binomial probability formula P(x = 0) where x represents the number of defective units.
- For all defective units, use the formula P(x = n), assuming n is the total number of units.
- For at least one good unit, one would calculate 1 - P(all defective units), which is P(x < n).