Possible spoiler (I don't know if my proof is correct)-- Algebraic numbers are countable, since their description is a countable combination of rationals which

Possible spoiler (I don't know if my proof is correct)-- Algebraic numbers are countable, since their description is a countable combination of rationals which are also countable. The measure of a countable set is zero, so the measure of its complement is 1, and thus the probability of choosing a transcendental is 1.