To find the probability that both balls drawn are of the same color, we first need to calculate the total number of ways to draw two balls from the box and the number of favorable outcomes where both balls are of the same color.

Total number of balls:
The total number of balls in the box is:
5 red + 4 blue + 6 green = 15 balls

Total number of ways to draw 2 balls:
The number of ways to choose 2 balls from 15 is given by the combination formula:

C(n, r) = n! / [r!(n – r)!]

So, the total number of ways to choose 2 balls from 15 is:

C(15, 2) = 15! / (2!(15 – 2)!) = (15 × 14) / 2 = 105

Number of favorable outcomes:
Now, we calculate the favorable outcomes where both balls are of the same color:

1. Red balls: The number of ways to choose 2 red balls from 5 is:

C(5, 2) = 5! / (2!(5 – 2)!) = (5 × 4) / 2 = 10

2. Blue balls: The number of ways to choose 2 blue balls from 4 is:

C(4, 2) = 4! / (2!(4 – 2)!) = (4 × 3) / 2 = 6

3. Green balls: The number of ways to choose 2 green balls from 6 is:

C(6, 2) = 6! / (2!(6 – 2)!) = (6 × 5) / 2 = 15

Total number of favorable outcomes:
The total number of favorable outcomes is the sum of the favorable outcomes for red, blue, and green balls:

10 (red) + 6 (blue) + 15 (green) = 31

Probability:
The probability is the ratio of favorable outcomes to total outcomes:

P(same color) = 31 / 105

Thus, the probability that both balls are of the same color is 31/105.

To find the probability that both balls drawn are of the same color, we first need to calculate the total number of ways to draw two balls from the box and the number of favorable outcomes where both balls are of the same color.

Total number of balls:
The total number of balls in the box is:
5 red + 4 blue + 6 green = 15 balls

### Total number of ways to draw 2 balls:
The number of ways to choose 2 balls from 15 is given by the combination formula:

C(n, r) = n! / [r!(n – r)!]

So, the total number of ways to choose 2 balls from 15 is:

C(15, 2) = 15! / (2!(15 – 2)!) = (15 × 14) / 2 = 105

### Number of favorable outcomes:
Now, we calculate the favorable outcomes where both balls are of the same color:

1. **Red balls**: The number of ways to choose 2 red balls from 5 is:

C(5, 2) = 5! / (2!(5 – 2)!) = (5 × 4) / 2 = 10

2. **Blue balls**: The number of ways to choose 2 blue balls from 4 is:

C(4, 2) = 4! / (2!(4 – 2)!) = (4 × 3) / 2 = 6

3. **Green balls**: The number of ways to choose 2 green balls from 6 is:

C(6, 2) = 6! / (2!(6 – 2)!) = (6 × 5) / 2 = 15

### Total number of favorable outcomes:
The total number of favorable outcomes is the sum of the favorable outcomes for red, blue, and green balls:

10 (red) + 6 (blue) + 15 (green) = 31

### Probability:
The probability is the ratio of favorable outcomes to total outcomes:

P(same color) = 31 / 105

Thus, the probability that both balls are of the same color is 31/105.