 Consider a random process that produces discrete outputs over an infinite period of time, e.g., the decay of atoms from a radioactive sample. Its output at regular time intervals is a string of digits—‘0’ if no atoms decay during a time interval, ‘1’ if one or more atoms decay during a time interval. A simple consideration shows that, with probability one, the sequence produced by our random process is not Turing-computable. There are uncountably many infinite strings of digits (even more strongly, there are uncountably many infinite strings of digits with any given limiting frequency of ‘0’s and ‘1’s). But there are only countably many Turing-computable infinite strings. Therefore, assuming that each infinite string has the same probability of occurring as a result of a random process, the probability that a random process would generate a Turing-computable string of digits is zero, whereas the probability that the string of digits is not Turing-computable is one (for the stronger conclusion that no such string of digits is Turing-computable, see Calude &amp; Svozil 2008). Thus, simply by using a truly random process to generate a string, we would have the physical means to go beyond what is Turing-computable. As Turing (1950, 438–439) pointed out, a machine with a “random element” can do “more” than a TM. But doing more is not the same as computing more. Contrary to what is sometimes suggested (e.g., Calude 2005, 10), the combination of a TM and a random process does not threaten Physical CTT.