Question

What are the chances of getting a free drink from a vending machine?

Answer 1

When purchasing a drink in the Generation III and IV games, there is a 1/64 chance that the player may also receive an extra drink for free. In Generation V, this chance is increased to a 1/32 chance. In Omega Ruby and Alpha Sapphire, there is also a chance of an extra drink, with an even slimmer chance of two extra drinks.

There is a 1/64 (1.56%) chance in Gens 3 and 4, and a 1/32 (3.1%) chance in Gen 5 to get double the drinks. It’s even possible in ORAS to get two free drinks, although the odds for that are unknown.

Source

Answer 2

In the Generation III, IV, and V games, when purchasing a drink, there
is a 3% chance that the player may also receive an extra drink for
free. When this happens, the message "Score! An extra can of [item]
dropped down!" or "Bonus! Another can of [item] dropped down." is
displayed, depending on generation

Source
See the trivia section.