Natalie has a bag that contains eight marbles. She draws out a marble, records its color, and puts it back.  

1. If Natalie repeats this eight times and does not record any red marbles, can she conclude that there are not any red marbles in the bag? Explain

   Hint (a):

   Is it possible that she drew the same marble every time?

2. If she repeats this $100$ times and does not record any red marbles, can she conclude that there are not any red marbles in the bag? Explain.

3. How many times would she have to draw marbles (putting them back each time) to be absolutely certain that there are no red marbles in the bag?

   Answer (c):

   No number of trials can absolutely prove that there are no red marbles in the bag.