Imagine a scenario where individuals are tasked with evaluating advertisements.
There are two categories of raters, and their behavior is independent from our perspective:
- **Careful Raters**: Comprising 80% of the group, they have a 60% likelihood of rating an ad as good and a 40% chance of rating it as bad.
- **Lazy Raters**: Making up 20% of the group, they consistently rate every ad as good, with a 100% probability.
1. If 100 raters each independently evaluate one ad, how many ads are expected to be rated as good?
2. If one rater evaluates 100 ads, how many ads are expected to be rated as good?
3. If an ad is rated bad, what is the probability that the rater was lazy?