When jousting, are minions drawn from your full deck or just the remainder?

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In a joust, each player has a random minion drawn from their deck for them and the mana cost of each compared to find a winner.
However, I'm curious to know if the draw pool for these cards is the full, original deck or just the cards left at the point the joust starts.
Or to put it another way: if my deck contains two copies of a minion and I've drawn and played them both during a game, can they be drawn again in the event of a joust?
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Edwin is my only minion. And I always draw him.
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