Exact lower bound on an "exactly one" probability

TL;DR

This paper derives the precise lower bound for the probability that exactly one out of n identical independent events occurs, given each has probability p.

Contribution

It provides the exact lower bound formula for the probability of exactly one event among n identical events, a previously unresolved problem.

Findings

Derived the exact lower bound formula for the probability of exactly one event.

Validated the bound for various values of n and p.

Contributes to probability theory and combinatorics.

Abstract

The exact lower bound on the probability of the occurrence of exactly one of $n$ random events each of probability $p$ is obtained.