FAQ: What's the other approach? How do I use probability alone?
The basic probability formula is, as we saw in the first method, (# of desired outcomes) / (# of possible outcomes). We can use that to find the probability of getting a desired number with each draw from the list.
We know we are looking specifically to get a 3, 6, 9, 12, or 15 each time, so there are 5 possible numbers which would give us that "success." Altogether, there are 7 numbers in the list, so the chance of getting a number that's divisible by three is 5/7.
The chance of getting a "success" on the second draw is 4/6, because we have one less number in the list (no replacement).
Similarly, the chance on the third draw is 3/5. If we want to find the probability of two or more events coming to pass, we want to multiply the probabilities together. That's 5/7 * 4/6 * 3/5 = 60/210 = 2/7