That's what I was talking about.

Largerichard did pretty much what I did. Though I concidered myself going first so I only draw 3 cards before mullagin. Speeddemon608 see the problem I was facing that you can't just multiply the chances to draw the two different cards because things gets weird with mulligan and the possibility of getting one or the other card in the first hand.

To more clearly specify the question then;
The deck has 2 doomsayers and 2 frost novas. You're going first, what's the probability of drawing at least one of each card by turn 5?

Of course you could further complicate things by considering other carddraw effects. Could be interesting to know if you benefit from agressively mulliganing for doomsayer/frostnova or if you end up with a larger possibility if you keep an arcane intellect?