To calculate the probability of drawing an even numbered card from a stack of 24 cards numbered 1 to 24, keeping it, and then drawing another even numbered card, we can follow these steps:
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Count the even numbered cards: In the range of 1 to 24, the even numbers are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, and 24. There are a total of 12 even cards.
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Calculate the probability of drawing the first even card: When we draw the first card, there are 24 cards total, and 12 of them are even. So, the probability of drawing an even card first is: \[ P(\text{first even}) = \frac{12}{24} = \frac{1}{2} \]
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After drawing one even card: After drawing and keeping one even card, there are now 23 cards remaining in the stack (24 - 1 = 23), and there will be 11 even cards left (12 - 1 = 11).
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Calculate the probability of drawing a second even card: The probability of then drawing another even card from the remaining 23 cards is: \[ P(\text{second even} | \text{first even}) = \frac{11}{23} \]
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Combine the probabilities: The overall probability of both events (drawing the first even card and then drawing a second even card) is: \[ P(\text{first even and second even}) = P(\text{first even}) \times P(\text{second even} | \text{first even}) = \frac{12}{24} \times \frac{11}{23} = \frac{1}{2} \times \frac{11}{23} = \frac{11}{46} \]
Thus, the final answer, which is the probability of drawing an even numbered card, keeping it, and then drawing another even numbered card from the stack, is:
E. \( \frac{11}{46} \)