Let's say I have three bins of red and blue balls. Each bin has exactly 1000 balls in it, but the problem is that I don't know exactly how many balls there are of each color in the three bins. I only have time to sample 100 balls from each bin, and I want to know how many red and blue balls there are in total across all the bins.
So what I do is I take 100 balls from bin A, find the percentage of red and blue balls there (let's say I count 20 red and 80 blue). I do the same for bin b (30 red, 70 blue), and bin C (40 red, 60 blue). From this I infer that each bin contains (to within some margin of error):
Bin A: 200 red, 800 blue
Bin B: 300 red, 700 blue
Bin C: 400 red, 600 blue
And then from that I infer across all three bins: 900 red, 2100 blue.
My question is: is this a reasonable way to proceed? Is there a better way to go? Is there something wrong with this line of inference? What would you do?