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Have you seen this question before?

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 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 come up with a rule for classifying raters as careful or lazy?

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