Prove that There is at least $2n-3$ distinct sum via probabilistic methods

Question

Suppose that $A$ is a set of size $n$

Define $A+A$ as sum of two distinct members of $A$

Prove that $|A+A| \ge 2n-3$ and equality holds for arithmetic progression.

The question is an exercise of probabilistic methods in combinatorics and it's assumed to solve this way