Let's see what's happening with each extraction, in terms of favourable cases vs total cases:
With the first extractions, you have 12 marbles, and 9 of them are blue. The probability of extracting a blue one is thus
[tex] \cfrac{9}{12} = \cfrac{3}{4} [/tex].
With the second extractions, you have 11 marbles (we don't replace the first one!), and 8 of them are blue (we already picked one!). The probability of extracting a blue one is thus
[tex] \cfrac{8}{11}[/tex].
Finally, you have 10 marbles, and 7 of them are blue (we already picked two!). The probability of extracting a blue one is thus
[tex] \cfrac{7}{10}[/tex].
If you want events to happen one after the other, you have to multiply their probabilities, so the answer is
[tex] \cfrac{3}{4} \cdot \cfrac{8}{11} \cdot \cfrac{7}{10} = \cfrac{168}{440} = \cfrac{21}{55}[/tex]
