Calculate probability of drawing at least 3 objects given certain conditions (in body paragraph)

Just need some help solving this question, the "at least 3" instead of "exactly 3" makes this difficult, I'm not sure where to start.

Assume there are 8 bags in front of you, all containing marbles of varying colours. The probability, per bag, of randomly picking a red marble, for bags #1 through #7 is 2%, while the probability of randomly picking a red marble in bag #8 is 1%. What is the chance you will pick at least 3 red marbles, if you're picking exactly one marble from each bag, randomly?

• Consider instead the probability of the complementary event (at most $2$ reds). You can case it as $$(0,0),(1,0),(0,1),(1,1),(2,0)$$ where the pair $(x,y)$ represents the outcome $x$ reds total from bags $1$ to $7$, and $y$ reds from bag $8$. – quasi Oct 12 '18 at 22:39
• If you can't even start, begin by calculating the probability of drawing all red marbles. – samerivertwice Oct 20 '18 at 2:24