Consider a company that manufactures electronic devices. The probability that a device is defective is 0.05. Given that a device is defective, the probability that it fails the quality test is 0.8. Conversely, if the device passes the quality test, what is the probability that it is not defective? This scenario illustrates the concept of conditional probability.

Let:

• $D$ = event that a device is defective
• $F$ = event that a device fails the quality test

Using the law of total probability and Bayes’ theorem, we are to find the conditional probability $P(D^c | F^c)$, where $D^c$ represents the event of a device not being defective and $F^c$ represents the event of a device passing the quality test.