To find the probability that all three marbles drawn from the bag are blue, we start by determining the total number of marbles in the bag.
The bag contains:
- 3 red marbles
- 6 blue marbles
- 4 green marbles
The total number of marbles is:
\[ 3 + 6 + 4 = 13 \]
Next, we need to calculate the total number of ways to choose 3 marbles from the 13 marbles, which can be calculated using the combination formula:
\[ \binom{n}{k} = \frac{n!}{k!(n-k)!} \]
where \( n \) is the total number of items, and \( k \) is the number of items to choose.
The total ways to choose 3 marbles from 13 is:
\[ \binom{13}{3} = \frac{13!}{3!(13-3)!} = \frac{13 \times 12 \times 11}{3 \times 2 \times 1} = 286 \]
Now, we need to find the number of ways to choose 3 blue marbles from the 6 available blue marbles. The number of ways to choose 3 blue marbles is:
\[ \binom{6}{3} = \frac{6!}{3!(6-3)!} = \frac{6 \times 5 \times 4}{3 \times 2 \times 1} = 20 \]
Now, to find the probability of drawing 3 blue marbles, we can use the formula for probability:
\[ P(\text{all blue}) = \frac{\text{Number of ways to choose 3 blue}}{\text{Total ways to choose 3 marbles}} = \frac{\binom{6}{3}}{\binom{13}{3}} = \frac{20}{286} \]
We can simplify this fraction:
\[ \frac{20}{286} = \frac{10}{143} \]
Next, we convert this fraction to a decimal for calculating the probability:
\[ \frac{10}{143} \approx 0.0699301 \]
Finally, to express this probability to the nearest thousandth, we round 0.0699301:
\[ 0.0699301 \approx 0.070 \]
Therefore, the probability that all three marbles drawn will be blue is:
\[ \boxed{0.070} \]