Algorithm for iterating over random permutation

I have a bag that has the following:

• 6 red marbles
• 5 green marbles
• 2 blue marbles

I want to remove a random marble from the bag, record it color, and repeat until no more marbles are left in the bag:

1. sort the counts
   • bag = {2:blue, 5:green, 6:red}
2. compute the cumulative counts
   • cumulative = {2:blue, 7:green, 13:red}
3. pick a random number in [0, max cumulative count]
   • rand(0, 13) = 3
4. find insertion point index of this integer using binary search
   • i = 1
5. record the color corresponding to this index
   • green
6. reduce that count by 1
   • bag = {2:blue, 4:green, 6:red}
7. repeat until no more marbles in bag

Is this a good way to do this or are there more efficient ways in terms of time complexity?