The process you describe doesn't address the problem. But again you need two sets of 100 experiments. In the first set you look in both boxes. Again you need two sets of 100 experiments. In the first set you look in both boxes.
Interference patterns are a whole new ball game.
Where you are refering to is the two slit experiments with single photons. The two slit experiment comes with at least three sets of 100 experiments. Slit A open. Slit B closed. Result 100 dots in normal distribution.