Let’s say we use people to rate ads.

There are two types of raters. Random and independent from our point of view:

• 80% of raters are careful and they rate an ad as good (60% chance) or bad (40% chance). 
• 20% of raters are lazy and they rate every ad as good (100% chance).

1. Suppose a rater rates just three ads, and rates them all as good. What’s the probability the rater was lazy?

2. Suppose a rater sees $N$ ads and rates all of them as good. What happens to the probability the rater was lazy as $N$ tends to infinity?

3. Suppose we want to exclude lazy raters. Can you devise a rule to classify raters as careful or lazy for a given significance level $\alpha$?