There are 10+7+9=26 marbles. There are 10 red marbles. 
Therefore 10 times out of 26 we will draw a red marble 
first.  That's 10/26ths of the time or 5/13ths of the 
time.

Of those 5/13ths of the time that we draw a red marble
first, we don't put it back and so there are only 25
marbles of which 9 are black.  So 9 times out of 25, or
9/25ths of those 5/13ths of the time we will draw a 
black marble second.

So we will succeed 9/25ths of 5/13ths of the time.

That's   

So we will succeed 9/65ths of the time.

Edwin