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I'm trying to figure out the percentage chance to draw a card based on the information below.

The deck has 30 cards. 2 of them are Aces and I just need to get 1 of them in my hand.

The draw goes like this, I draw 4 cards and if I don't have an ace I can put those 4 cards on the bottom (so no chance of being re-drawn yet) and draw 4 more.

After this the deck is shuffled and I get to draw 1 more card.

With these interactions in mind what is the percentage chance I draw an Ace with this sequence?

I believe the chance are as follows but i may be forgetting something

Draw 1 = 2/30

Draw 2 = 2/29

Draw 3 = 2/28

Draw 4 = 2/27

Draw 5 = 2/26

Draw 6 = 2/25

Draw 7 = 2/24

Draw 8 = 2/23

Draw 9 = 2/26

I for the life of me can't figure it out and would love to know the method to figure it out.

Thanks in advance.