Standard deviation for a binomial distribution

There are N boxes which can be empty or filled with balls.
The probability of filling each box with a ball is p.

According to binomial distribution, the mean no. of boxes filled should be Np and the standard deviation would be sqrt[N(1-p)p].

If there are two series of such boxes and each serie has N boxes.
The new variable is the ratio of number of the ball-containing boxes in the two series.
After each round, the boxes would be emptied and filled again.
What is the expected ratio? and What is the standard deviation for this ratio?

Thanks for the great help.
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