Heres another way to figure the first one.
We've have drawn 2 of 52 cards in the deck so there are 50 left.
So the total number of sets possible in picking the next three is just C(50,3).
And since we have picked two red cards, there are 24 left. And we wnat to choose any 3 of them = C(24,3)
So the probability that the next three cards are red is: C(24,3) / C(50,3) = 0.103265306122449
As Melody found.......
The second one is similarly figured....it would be C(11,3) / C(50,3) = 0.0084183673469388
Again.....as Melody found......
