Generating an uncomputable number by throwing dice

Question

If I were to roll a die infinitely many times, assuming the result was truly random, and use the results as the decimal places of a number, would that number (likely) be an uncomputable number?

Answer 1

Yes. There are only countably many computable numbers (because there are only countably many computer programs), so a random real number, say in the interval $[0, 1]$ to be concrete, is uncomputable with probability $1$.

In fact with probability $1$ it will have a much stronger property called algorithmic randomness, which roughly speaking says that the digits are incompressible.