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First let's find the probability of drawing a red marble.  I know that the probability is my (# of red marbles)/(total # of marbles) so 8/20 which we can simplify to 2/5.
 
Since the first marble is put back, I know that I will still have 20 total marbles.  Therefore the probability of drawing a white marble is (# of white marbles)/20 which is 4/20.  We can simplify this to 1/5.
 
The probability of drawing a red marble and then a white marble is going to be the product of these probabilities.
 
Therefore the total probability is the probability of the first even occurring times the probability of the second event occurring.
 
(probability of red)*(probability of white) = total probability
(2/5)*(1/5)=2/25
 
So we can expect to draw a red marble then a white marble 2 out of 25 times that we perform this experiment.
 
Hope this helps!