Final answer:
The probability that all three marbles drawn will be green is 1/56.
Step-by-step explanation:
To find the probability that all three marbles drawn will be green, we need to determine the number of favorable outcomes and the total number of possible outcomes. In this case, there are 7 green marbles out of a total of 16 marbles in the bag.
So, the probability of drawing a green marble on the first draw is 7/16.
Since we are drawing without replacement, the probability of drawing a green marble on the second draw is 6/15, and on the third draw it is 5/14.
To find the overall probability, we multiply the probabilities of each draw:
Probability = (7/16) * (6/15) * (5/14) = 1/56