Answer
1/64, 5/16
Work Step by Step
We see that there are $2^6=64$ possible options.
a) Only one of these options will result in all molecules being on one side of the box. Thus, the answer is 1/64.
b) We find that the number of possible ways this could happen is:
$ \frac{6!}{3!3!}$
This gives:
20
So, our answer is:
$20/64=5/16$
