A hypothetical
scenario. You
are dropped into a tube that is several miles long, end to end. You
start at
one end at 5 AM, and you begin to make your way towards the other end.
As you
go, sometimes you move quite fast and sometimes you slow down. Once in
a while
you stop to rest. You make it to the other end by 5 PM. You sleep. Now
it is
the next morning, 5 AM again, and you begin the trip back to the end
you started
at the previous day. Again, you trip varies in speed, and sometimes you
even
stop. You make it back to the beginning at 5 PM. What is the chance (in
a
percent form) that you were at some same spot in the tube at the same
time on
both days?