Hi Bill, you keep making the same mistake. 10^-11 is not the probability, and one certainly would not multiply this as you do to estimate the likelihood of getting a bifunctional protein.
To illustrate, starting again with a scenario (the current biosphere) in which 10^20 new proteins arise each day. The numbers of ATP-biinding proteins in this collection would be about 10^9, and the probability that any of these would be bifunctional would be calculated from the ratio obtained by dividing 10^9 by 10^11 (NOT 10^11 squared). Thus, for example, in a year, the probability of getting a bifunctional protein would be 1, not some unseemingly low number.
I am curious, why do you cling to a scenario wherein one and only one protein comes about? This makes no biological or chemical sense, and leads to lots of irrelevant calculations.