Are the containers full or empty?
First Container: Full
Second Container: Full
First, we cut about 100 small squares of paper and makes two piles of 50 pieces.
We labeled each set 1-50. Next we found some container that we
could use to put the pieces of paper in. From our first
set of 50 numbers, we put in the pieces labeled 1-10 and drew out the number
1. We continued with the process until all 50 pieces were in and the
numbers 1-5 were drawn as stated in the directions to the first container.
The process was repeated for the second container except this time
we drew out the multiples of 10.
Students may include drawings here to illustrate.
We still think that both containers are full.
We were right about the second container but the first container was tricky.
It seemed that there would still be some numbers left if you stopped
at some point.
So, the first container is empty because we can not name a number that would
be left, and the second is full because there are many numbers that
we could name that would be left. It is pretty cool that probability can be used as a tool to prove ideas about infinity.