Probability question

  (Edited: )

I thuroughly enjoyed yesterdays 3rd segment with probability calculations and would like to pose a followup question to Day9, if he reads this, or the community if he doesn't want to do another math segment.

Yesterday we calculated probabilities of drawing a single card out of 2 in 30. What I would find more interesting is calculating the chance of drawing 2 cards by a specific turn. Many decks hinges on combos and those that require 3+ cards usually compensate by being all about card draw.

Question. I need to draw Doomsayer+Frost nova for a turn 5 play for this freeze mage to survive against aggro. How likely am I to do so?

I started out with the numbers and methods Day9 used yesterday. Getting the chances of either one card being drawn in first hand, then mullagain+5 turns and came to about 36.6% chance BUT realised I was doing it wrong.

Since we're calculating on both cards the probability starts to change if we actually draw one of them, at least in the first draw, right? Because if one of the first 3 cards is a doomsayer then we only have a 2 card mullagain.

I'm guessing you could do it with this method but then having to make a full calculation for every draw possibility that includes drawing one of the desired cards? But that seems like it'd be very annoying to do.

Are there any useful formulas or methods for calculating probabilities like this or is it all about just adding and multiplying everything over and over?