I was learning about probability theory, with different events, until I came across something I wanted to query.
I wanted to check if the above picture means if I pick k = 3, then:
2026-04-04 20:38:54.1775335134
Repeated application of union bound
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Yes. As for why, consider a geometric interpretation:
The area contained in at least one of the sets (i.e. $\mathbb P(A \cup B \cup C)$) is no bigger than the sum of their individual areas (i.e. $\mathbb P(A) + \mathbb P(B) + \mathbb P(C)$).