To find the probability of randomly picking a blue marble, you need to divide the number of blue marbles by the total number of marbles.
The number of blue marbles is 3. The total number of marbles is:
\[ 10 \text{ (green)} + 7 \text{ (red)} + 3 \text{ (blue)} = 20 \text{ (total marbles)} \]
Now, the probability \( P \) of picking a blue marble is given by:
\[ P(\text{blue}) = \frac{\text{Number of blue marbles}}{\text{Total number of marbles}} = \frac{3}{20} \]
Now, convert this fraction to a decimal:
\[ \frac{3}{20} = 0.15 \]
Thus, the probability of randomly picking a blue marble is 0.15.