Probability Calculation:
To find the probability that both balls are the same color, we need to consider two scenarios: both balls are red or both balls are green.

Probability of both balls being red:
Out of the total 9 balls, 5 are red. So, the probability of selecting a red ball on the first draw is 5/9. After the first ball is drawn, there are 8 balls remaining, out of which 4 are red. So, the probability of selecting a red ball on the second draw, given that the first ball was red, is 4/8. Therefore, the probability of both balls being red is (5/9) * (4/8) = 20/72.

Probability of both balls being green:
Similarly, the probability of selecting a green ball on the first draw is 4/9. After the first ball is drawn, there are 8 balls remaining, out of which 3 are green. So, the probability of selecting a green ball on the second draw, given that the first ball was green, is 3/8. Therefore, the probability of both balls being green is (4/9) * (3/8) = 12/72.

Total probability of both balls being the same color:
Since there are only two possibilities (both balls being red or both balls being green), we can add the probabilities calculated above to find the total probability of both balls being the same color.

(20/72) + (12/72) = 32/72 = 4/9

Therefore, the probability that both balls are the same color is 4/9.

Explanation:
The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In this case, the favorable outcomes are selecting two balls of the same color (either red or green), and the possible outcomes are selecting any two balls from the bag.

To calculate the probability, we consider each color separately. We find the probability of selecting a ball of that color on the first draw, and then multiply it by the probability of selecting another ball of the same color on the second draw, given that the first ball was of that color. Finally, we add these probabilities together to get the total probability of both balls being the same color.

In this case, the probability of both balls being red is (5/9) * (4/8), and the probability of both balls being green is (4/9) * (3/8). Adding these probabilities gives us 4/9, which is the probability that both balls are the same color.