Let's go through the solution step-by-step:
1. Count the total number of balls in the bag:
- There are 4 red balls, 6 white balls, and 3 green balls.
- To find the total number of balls, add the number of red balls, white balls, and green balls.
[tex]\[
\text{Total number of balls} = 4 + 6 + 3 = 13
\][/tex]
2. Determine the number of non-white balls:
- Non-white balls are those that are either red or green.
- Add the number of red balls and green balls.
[tex]\[
\text{Number of non-white balls} = 4 + 3 = 7
\][/tex]
3. Calculate the probability of drawing a non-white ball:
- The probability of an event is given by the number of favorable outcomes divided by the total number of possible outcomes.
- Here, the favorable outcomes are drawing a non-white ball, and the total number of possible outcomes is drawing any ball.
[tex]\[
\text{Probability of drawing a non-white ball} = \frac{\text{Number of non-white balls}}{\text{Total number of balls}} = \frac{7}{13}
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{\frac{7}{13}}
\][/tex]
This shows that the probability of drawing a non-white ball from the bag is [tex]\(\frac{7}{13}\)[/tex]. Thus, the correct answer is option B.
