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You draw one card from a 52-card deck. Then the card is replaced in the deck and the deck is shumited, and you draw again. Find the probability of drawing a four each time. The probability of drawing a four each time is (Type an integer or a simplified fraction.)

Ask by Coles Bowman. in the United States
Mar 17,2025

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The probability of drawing a four each time is \(\frac{1}{169}\).

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Mind Expander

When drawing a card from a standard 52-card deck, there are 4 fours (four of hearts, diamonds, clubs, and spades). The probability of drawing a four on the first draw is \( \frac{4}{52} \), which simplifies to \( \frac{1}{13} \). Since the card is replaced and the deck is shuffled, the probability of drawing a four again on the second draw remains \( \frac{1}{13} \). To find the probability of both events occurring (drawing a four each time), we multiply the probabilities together: \[ P(\text{four on first draw}) \times P(\text{four on second draw}) = \frac{1}{13} \times \frac{1}{13} = \frac{1}{169}. \] So, the probability of drawing a four each time is \( \frac{1}{169} \).

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