Help with probability?

Playing Yugioh and I want to know the EXACT probability of getting out a certain monster (Herald) turn 1.

I have a 35 card Deck (yes I know min is 40, I have x3 Upstart, x1 One day of Peace, and x 1 Chicken Game, I immediately draw with these so the deck is systematically 35 cards). Calculate using a 35 card deck please.

If I draw a certain card in my Deck (Dogra), I can get out Herald with just drawing this card alone. I use 3 Dogra (max allowed)

If I draw Herald in conjunction with another specific card (Ritual Art), I can get out Herald. I use 3 Herald and 2 Ritual Art (max allowed).

Lastly, a card called Manju can summon Herald if, and only if, I already drew Herald or Ritual Art. I use 3 Manju (Max allowed).

So desired Combinations (I only need one of these to be successful):

At least 1 Dogra OR

At least 1 Herald WITH 1 Ritual Art OR

At least 1 Manju WITH Herald or Ritual Art (Just need on or the other with Manju, not both)

Also, if I draw multiple ways of getting out herald that's fine, just give me the probability of getting out AT LEAST 1 Herald on my opening hand.

I start out with a 5 card draw if I'm going first, 6 if I go 2nd (give me probability of both please).