To solve this problem, we will first calculate the probability that at least one of the drawn balls is green. This can be easier if we use the complementary event — that is, calculating the probability that neither of the two balls drawn is green, and then subtracting it from 1.

Step-by-Step Approach:

Step 1: Total number of balls

The total number of balls in the bag is the sum of red, green, and yellow balls: $9 \, (\text{red}) + 15 \, (\text{green}) + 11 \, (\text{yellow}) = 35 \, \text{balls}$

Step 2: Probability of drawing no green balls

To draw two balls with none being green, we must draw only from the red and yellow balls (which total $9 + 11 = 20$ balls). The probability of drawing two balls that are not green is as follows:

• First draw: The probability of not drawing a green ball (drawing from the 20 red or yellow balls) is: $\frac{20}{35}$
• Second draw: After one non-green ball has been removed, there are now 19 non-green balls left out of 34 remaining balls. The probability of drawing another non-green ball is: $\frac{19}{34}$

Thus, the probability of drawing two balls with no green balls is: $P(\text{no green}) = \frac{20}{35} \times \frac{19}{34} = \frac{380}{1190}$

Step 3: Probability of drawing at least one green ball

Now, we subtract the probability of drawing no green balls from 1: $P(\text{at least one green}) = 1 - P(\text{no green}) = 1 - \frac{380}{1190} = \frac{1190 - 380}{1190} = \frac{810}{1190}$

So, the probability that at least one of the two balls drawn is green is: $P(\text{at least one green}) = \frac{810}{1190} \approx 0.6807$

Final Answer:

The probability that at least one of the drawn balls is green is approximately 0.6807 or 68.07%.

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Would you like a more detailed breakdown of any of the steps, or do you have other questions on this topic?

Here are some related questions you might find interesting:

1. What is the probability that both drawn balls are red?
2. What is the probability that both balls drawn are yellow?
3. How does the probability change if the balls are replaced after each draw?
4. How do you calculate the probability of exactly one green ball being drawn?
5. What would happen if there were 5 more green balls in the bag?

Tip: When calculating probabilities involving multiple events, always consider complementary events (the opposite of the event you're looking for) — it often simplifies the problem!