Computers and brains are modeled by finite and probabilistic automata, respectively. Probabilistic automata are known to be strictly more powerful than finite automata. The observation that the environment affects behavior of both computer and brain is made. Automata are then modeled in an environment. Theorem 1 shows that useful environmental models are those which are infinite sets. A probabilistic structure is placed on the environment set. Theorem 2 compares the behavior of finite (deterministic) and probabilistic automata in random environments. Several interpretations of Theorem 2 are discussed which offer some insight into some mathematical limits of machine intelligence.