The probability that a uniform random number on $[0, 1]$ is rational

Example · High school

Terms

Term	This example	Why
probability zero	✓	The event that a uniform random number on $[0, 1]$ is rational has probability zero, because $\mathbb{Q} \cap [0, 1]$ has measure zero. The event is not impossible, however, because every rational number in $[0, 1]$ is a possible outcome.

Distinctions using this example

• Types of set sparsity

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