In a standard deck of 52 cards, if two cards are drawn with replacement, what is the probability that both are aces?

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Multiple Choice

In a standard deck of 52 cards, if two cards are drawn with replacement, what is the probability that both are aces?

Explanation:
Drawing with replacement keeps the deck the same for both draws, so the two events are independent. The chance to get an ace on a single draw is 4 out of 52, which is 1/13. Since the second draw is the same situation, multiply the probabilities: (1/13) × (1/13) = 1/169. Without replacement, the second draw would have a different probability (3/51), which would give 1/221, but with replacement the correct probability is 1/169.

Drawing with replacement keeps the deck the same for both draws, so the two events are independent. The chance to get an ace on a single draw is 4 out of 52, which is 1/13. Since the second draw is the same situation, multiply the probabilities: (1/13) × (1/13) = 1/169. Without replacement, the second draw would have a different probability (3/51), which would give 1/221, but with replacement the correct probability is 1/169.

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