A bag contains 8 red marbles, 5 blue marbles and 7 green marbles. If three marbles are drawn out of the bag, what is the probability, to the nearest 1000th, that all three marbles drawn will be green?

To solve this problem, we need to use the concept of probability.

Step 1: Calculate the total number of marbles in the bag. The total number of marbles is 8 red + 5 blue + 7 green = 20 marbles.

Step 2: Calculate the probability of drawing the first green marble. The probability of drawing a green marble on the first draw is the number of green marbles divided by the total number of marbles, which is 7/20.

Step 3: Calculate the probability of drawing the second green marble. After one green marble has been drawn, there are now 6 green marbles left and 19 total marbles. So, the probability of drawing a green marble on the second draw is 6/19.

Step 4: Calculate the probability of drawing the third green marble. After two green marbles have been drawn, there are now 5 green marbles left and 18 total marbles. So, the probability of drawing a green marble on the third draw is 5/18.

Step 5: Calculate the overall probability of drawing three green marbles in a row. The overall probability is the product of the individual probabilities, so we multiply the three probabilities together: (7/20) * (6/19) * (5/18) = 0.035 or 0.035 to the nearest thousandth.

So, the probability that all three marbles drawn will be green is 0.035 or 3.5%.