Please, bear with me if this is too stupid.

Let's have a basket with 400 balls. Clairvoyant claims she can guess which balls we take out without looking. So we take 50 out (mark them secretly), return them back and then she takes say 65 out. They are not the same so we say she's a fraud but she says that she guessed at least some of them. We find that at the end she has 12 balls out that were selected also by us before that. If all were random they should be approx. 8. Using Chi-square, one can calculate if 12 is a significant coincidence. What if she insists we repeat the experiment 10 times, every time taking out a different number of balls but generally less than 25%? Then in 4 out of 10 tests, the coincidence proves significant and in 4 other there is a weak trend. How do we summarize the results?
Thank you,