🃏 Drawing Cards: Two Aces from a Poker Deck
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Task:
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Two cards are drawn randomly from a poker deck of 52 cards. What is the probability that both drawn cards are aces?
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Step-by-step Solution:
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- Number of aces in the deck: There are 4 aces in a deck of cards.
- Combinations for 2 aces: \(C(4, 2) = 6\) ways to choose 2 aces.
- Combinations for 2 arbitrary cards: \(C(52, 2) = 1326\) ways to choose 2 cards from 52.
- Calculate probability: \(\frac{6}{1326} = \frac{1}{221} \)
- Decimal result: ≈ 0.0045
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Answer:
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The probability of randomly drawing 2 cards from a poker deck and getting two aces is about 1 in 221.
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⚙ karten