Final answer:
The exact probability that all three marbles drawn will be blue is 1/22.
Step-by-step explanation:
To calculate the probability of drawing all three blue marbles, we need to find the ratio of favorable outcomes to total outcomes. There are 5 blue marbles in the bag, and we need to draw 3 of them without replacement. The total number of marbles in the bag is 12 (3 red + 5 blue + 4 green).
So, the probability of drawing all three blue marbles is:
P(3 blue) = (5/12) * (4/11) * (3/10) = 60/1320 = 1/22
Therefore, the exact probability that all three marbles drawn will be blue is 1/22.