What is the probability of 5 cards out of 20 appearing?

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This is a Yu-Gi-Oh Duel Links question. It is a mobile application that allows you to duel other players with digital cards.

Only 2 copies of Card A exist in the 20 card deck.

Only 3 copies of Card B exist in the 20 card deck.

Card B can search for Card A.

What is the equation to determine the probability/likelihood of seeing Card A in a 20 card deck?

For example Card A is your win condition, and subsequentlly, drawing card B is also your win condition (since Card B searches for Card A). Drawing any copy of Card A or Card B in your opening hand is your win Condition.

You can only draw 4 cards in your opening hand.

For simplicity, the sample size thresholds can be [100] [1,000] [10,000]

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Let X be the event that either card A or card B is drawn. Then, P(x) = $2/20 + 3/20 = 1/4$