These two events are dependent.

Explanation:

The two events involve the same population (TV viewers) watching your favorite show. The outcome of the first event (the selection of the first viewer) can affect the outcome of the second event (the selection of the second viewer), especially since the second selection is influenced by the first one.

For example, if the first viewer is selected from a group of people already known to be watching the show, then the chances of selecting another viewer watching the same show could be affected by the first selection. The two selections are not independent because there is a relationship between them.

However, if the total number of TV viewers is large and the proportion of people watching your favorite show is small, we could use the 5% guideline. If less than 5% of the total TV viewers are watching the show, the two selections could be treated as independent. But without that specific information, they remain dependent by default.

Questions to consider:

1. What is the total number of TV viewers versus the number watching the show?
2. How does the population size affect the likelihood of treating the events as independent?
3. Can the 5% guideline apply in this context?
4. How do dependent events differ from independent events in probability?
5. In real-world scenarios, when would you expect events to be independent?

Tip: For large populations, you can often approximate dependent events as independent if the sample size is small compared to the population, which is when the 5% rule is useful.