Answer: If the product of any two numbers in the list is equal to 0, you can't conclude that the list is composed only by zeroes. In fact, suppose that you have a list of N numbers which are all zeroes except one. Whenever you multiply two elements of this list, you either multiplies two zeroes, or you multiply the non-zero element by a zero element, and so the result is zero, but the list is not composed by zeroes only.
This is theoretical probability. The 7 pieces of paper each bear one number from {1, 2, ... , 6, 7}. There is only one piece of paper marked 7. So the probability of drawing a 2 is 1/7.
