To calculate the probability of pulling out a blue marble, we first need to find the total number of marbles in the bag. We can do this by adding up the number of marbles of each color:
- Red marbles: 6
- Blue marbles: 3
- Yellow marbles: 7
- Green marbles: 5
Now, let's calculate the total number of marbles:
\[ \text{Total marbles} = 6 + 3 + 7 + 5 = 21 \]
Next, we find the probability of pulling out a blue marble. The probability \( P \) of an event is calculated as the number of successful outcomes divided by the total number of possible outcomes. In this case, the successful outcome is drawing a blue marble.
So, the probability \( P(\text{blue}) \) is:
\[ P(\text{blue}) = \frac{\text{Number of blue marbles}}{\text{Total number of marbles}} = \frac{3}{21} \]
Now, we can simplify this fraction:
\[ P(\text{blue}) = \frac{3}{21} = \frac{1}{7} \]
To convert this fraction into a percentage, we can divide 1 by 7 and then multiply by 100:
\[ \frac{1}{7} \approx 0.142857 \quad \text{(approximately)} \] \[ 0.142857 \times 100 \approx 14.2857% \]
Rounding to the nearest tenth gives us approximately \( 14.3% \).
So, the probability that the marble will be blue is:
14.3%