This thought experiment was presented to me the other day.
Jar A has 100 red marbles and jar B has 100 blue marbles. If you take a handful of marbles out of jar A and put them in jar B and take a handful of marbles out of jar B and put them in jar A, which jar would have more of the non-original coloured marbles. A handful is an arbitrary constant, so both jars end up with 100 marbles but you don't know how many were transferred. So for example would jar A have more blue marbles than jar B has red marbles.
The correct answer is they always will have the same amount. I can see that this is true, but I don't know why this is true. When I thought about it I thought jar B would have more non-original marbles because when red marbles are put in B, some of those red marbles may be taken back out (when a handful is taken from jar B) and put back to jar A. Why is it wrong to use probability in this situation?
Another student commented, "I got the answer wrong because I used math". This statement is a falsehood because the wrong mathematical technique was used, right? Or does sometimes math fail us?