What is the law of large numbers?
PICTURE THIS: DATA SPLIT
Fit on train, tune on val, report on test once.
Simple meaning
The law of large numbers says sample averages converge to the expected value as independent observations accumulate.
WHY — Probability instead of guessing?
Why interviewers care about Probability:
who only read docs from people who shipped.
and tied to Data Science work.
Name the idea, why it exists, then one short example.
End with when you use it and one common pitfall.
STEPS — What happens step by step?
Before you speak the answer, walk the interviewer through these steps:
- 1The law of large
numbers says sample averages converge to the expected value as independent observations accumulate.
- 2It justifies why larger
A/B tests stabilize conversion rates.
- 3It does not say
a losing streak must be balanced immediately, which is the gambler's fallacy.
- 4Give an example
One tiny concrete case you can say aloud.
- 5Common mistake
What juniors usually get wrong.
- 6Close
When you pick this over the alternative.
EXAMPLE — See it in action
Here's a short line you can speak, broken into clear beats:
Note: Adapt this scaffold to your own project — keep it under 60–90 seconds.
Key takeaway
The law of large numbers says sample averages converge to the expected value as independent observations accumulate. It justifies why larger A/B tests stabilize conversion rates.