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In the given problem, we are dealing with semiconductor chips, specifically a lot of 100 chips containing 20 defective ones. Defective chips are those that do not meet the required specifications and hence cannot be used effectively in their intended applications.
Understanding the concept of defective chips is crucial in quality control processes. When a batch contains defective chips, it's important to identify them to prevent faulty products from reaching consumers. In our exercise, knowing the portion of defective chips is key to calculating probabilities involved when selecting them randomly.
For any similar problems, always start by identifying the total number of items and how many of those are defective. This will guide the initial steps in determining the probability for picking a defective item.

Conditional probability is the probability of an event happening given that another event has already occurred. In simpler terms, it's figuring out the likelihood of something given some prior knowledge.
In the case of our chips, if we know that the first chip selected is defective, it influences or changes our calculation of getting a second defective chip. After removing one defective chip, there are now 19 defective chips left out of 99.

• Given the first chip is defective: the conditional probability becomes \( P(\text{Second is defective} | \text{First is defective}) = \frac{19}{99} \)

This is a classic example of how conditional probability can adjust our calculations when figuring out the odds under certain conditions. Understanding this concept can enhance decision-making in uncertain situations.

This rule is used when we need to find the probability of two independent events happening together. However, in scenarios where one event affects the outcome of another, as in our case, the events become dependent.
When calculating the probability of both chips being defective, we observe that the probability of the second event depends on the outcome of the first. That's why:

• The formula becomes: \[ P(\text{Both are defective}) = P(\text{First is defective}) \times P(\text{Second is defective} | \text{First is defective}) \]
• Substituting the values we calculated earlier: \[ \frac{1}{5} \times \frac{19}{99} = \frac{19}{495} \]

This illustrates the multiplication rule for dependent events, highlighting the importance of acknowledging the nature of the events at play. It's essential in real-life applications where multiple events interact.