Ad Raters

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 we have 100 raters each rating one ad independently. What’s the expected number of good ads?

2. Now suppose we have 1 rater rating 100 ads. What’s the expected number of good ads?

3. Suppose we have 1 ad, rated as bad. What’s the probability the rater was lazy?