Sentence examples for vanishingly small probability from inspiring English sources

"The universe is in fact constructed so that these coincidences are unavoidable: the extraordinarily unlikely must happen; events of vanishingly small probability will occur," he writes.

Because deleterious mutations have a vanishingly small probability of becoming fixed in a population, most substitutions (i.e., fixed mutations) would be neutral.

We can mathematically roll up all these vanishingly small probabilities and calculate the new odds of winning the jackpot on a single initial ticket purchased: one in 40,665,099.

Further, it correctly limits the variance to non-negative values, and assigns vanishingly small probabilities to a variance of zero.

Thus, the third surface can be achieved with vanishingly small error probability.

For example, if we set (that implies ) and, then we achieve the following rates with vanishingly small error probability: (E.12).

then all users can decode both the common message and the independent message directed to itself with vanishingly small error probability.

It is straightforward to see that if the following conditions are satisfied, then both users can decode the messages directed to themselves with vanishingly small error probability.

As of now, we showed that all rates in the so-called capacity region are achievable with vanishingly small error probability, however we did not claim anything about the secrecy conditions which will be considered next.

Surely, this probability is vanishingly small.

In the Appendix, I provide a rough, toy calculation of the upper bound of the probability of the emergence of a coupled replication-translation system in an O-region – this probability is, indeed, vanishingly small.