x.com/suchenzang/status/2056450518206361964
1 correction found
if you're top 10% in 3 different areas, that already makes you top 0.1%
This percentile math is not automatic. Multiplying 10% × 10% × 10% only gives 0.1% when the three traits are statistically independent, which the post does not establish.
Full reasoning
The statement treats the overlap of three "top 10%" groups as if it must equal 0.1%. That is not true in general.
Standard probability rules say the general formula for overlap is P(A and B) = P(B)P(A|B), not simply P(A)P(B). The product rule P(A and B) = P(A)P(B) applies only when the events are independent. The same logic extends to three events: multiplying 0.1 × 0.1 × 0.1 is valid only if being top-10%-level in each area is independent of being top-10%-level in the others.
But skill areas are often correlated rather than independent. So being top 10% in three areas does not automatically make someone top 0.1% overall. As a simple counterexample, if the same 10% of people are top 10% in all three areas, then the overlap is 10%, not 0.1%.
So the claim is incorrect as written because it presents a conditional probability result as an automatic one.
2 sources
- 5 Independent Events - STAT 414 | Introduction to Probability Theory
Def. 5.2 (Independent Events) Events A and B are independent events if and only if: P(A∩B)=P(A)×P(B). Otherwise, A and B are called dependent events.
- 3.3 Two Basic Rules of Probability - Introductory Statistics 2e | OpenStax
If A and B are two events defined on a sample space, then: P(A AND B) = P(B)P(A|B). If A and B are independent, then P(A|B)=P(A). Then P(A AND B)=P(A)P(B).