A percentage would be a value between 0 and 1, so, for 75% we would have

chance = 0.75
-- or
chance = 75 / 100

To "roll the dice," (so to speak) we generate a random number between 0 and 1:

randomNumber = math.random()

That randomNumber will be less than chance chance amount of the time (e.g., a random number from 0 to 1 is less than 0.35, well, 35% of the time).

So that is our check:

if randomNumber < chance then
    -- only occurs with `chance` probability
end

(Or inline)

if math.random() < 0.75 then
    -- only occurs 3/4 of the time
end

Explanation of using math.random with different arguments for this purpose:

math.random(a,b) returns a random integer between a and b (inclusive).

So, for 75% chance, we could use these:

    math.random(1,4) <= 3 
    math.random(1,100) <= 75

However, if we wanted to use 75.9%, this doesn't work:

    math.random(1,4) <= 3.036
    -- math.random(1,4) only returns 1, 2, 3, or 4.
    -- So this is no different than just `math.random(1,4) <= 3` (75%)
    math.random(1,100) <= 75.9
    -- Same problem: same as 75%

However, math.random() with no argument generates any number between 0 and 1.

Here's sample output:

0.84018771715471
0.39438292681909
0.78309922375861
0.79844003347607
0.91164735793678

It provides numbers as dense as possible, so we don't have the problems of only generating integers now.

    math.random() < .75
    -- works just as well as
    math.random() < .759

You might notice that this is actually pretty much equivalent to just dividing by the appropriate power of 10, e.g., for our 75.9% example, we could have used:

    math.random(1,1000) <= 759

However, that starts to get messy. Especially with long decimals. What if we wanted a 1 in math.pi chance?

if math.random(1,10000000000) <= 3183098861 then

which is just getting ridiculous (and is also not to the full precision it could be). Much more elegant to use:

    math.random() < 1 / math.pi