*returning the marble into the bag after each draw.*

I'm wondering, though -- how does performing the test in this manner differ from simply having them dump all the marbles out and count the

*actual*numbers and doing the Chi-square test with those exact values? If you do a Chi-sq test on flipping a coin, for example, this seems to be similar to returning the marble after each draw. They are all independent events. So, hopefully my question makes sense -- how does the Chi-square test "change" between these two scenarios? Does it?

Thanks. Please note, I am no mathematician.