A bag contains 7 red​ marbles, 4 blue​ marbles, and 3 green marbles. What is the probability of choosing a blue marble when one marble is​ drawn?

To find the probability of choosing a blue marble from the bag, we first need to determine the total number of marbles in the bag.

The bag contains:
- 7 red marbles
- 4 blue marbles
- 3 green marbles

Now, we can add these together to find the total number of marbles:

\[
\text{Total number of marbles} = 7 + 4 + 3 = 14
\]

Next, we want to find the probability of drawing a blue marble. The probability of an event is given by the formula:

\[
P(\text{Event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}
\]

In this case, the number of favorable outcomes (blue marbles) is 4, and the total number of outcomes (total marbles) is 14. Therefore, the probability of drawing a blue marble is:

\[
P(\text{Blue marble}) = \frac{4}{14}
\]

We can simplify this fraction:

\[
P(\text{Blue marble}) = \frac{2}{7}
\]

Thus, the probability of choosing a blue marble when one marble is drawn is \(\frac{2}{7}\).