Answer:
0.015
Explanation:
We want to know that probability that we draw a green marble for the first AND the second AND the third draws. The act of drawing each marble changes the probabilities of the next draw, so we say that these events (drawing green marbles) are dependent. Mathematically, this means we'll be multiplying the probabilities of each event to get the probability of the whole thing. I'll denote the first, second and third green marble drawing events as A, B, and C.
For our first drawing, we have 5 possible green marbles to pick from out of 4 + 8 + 5 = 17 total marbles, so P(A), the probability of drawing a green marble, is 5/17.
Now, A, B, and C all represent the event of drawing a green marble, but the way they depend on one another is important here. If we want B to be our second draw, it'll depend on what happens in our first draw, A. We call this kind of probability conditional, and we write it as P(B | A), the conditional probability of event B after event A's occurred.
Here, event A is "drawing a green marble." What happens during event A? Well, we draw a green marble, so we have one fewer green marble, and one fewer marble altogether. Our chance of drawing a green marble after event A, P(B | A), is 4/16 or 1/4 then, since we now have 4 green marbles and 16 total marbles.
Using that same reasoning, P(C | B), the probability of event C (drawing a green marble) after event B has occurred, is 3/15, or 1/5, since we'll have 3 green marbles out of 15 total after drawing our second during event B.
Multiplying these all together, we have
P(A) · P(B | A) · P(C | B) = 5/17 · 1/4 · 1/5 = 1/68 ≈ 0.015