To find the probability of selecting a historical fiction book first and then a romance novel second, we need to calculate the probabilities step by step.
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Selecting a historical fiction book first:
- There are 12 historical fiction books out of a total of 50 books.
- The probability of selecting a historical fiction book first is: \[ P(\text{Historical Fiction first}) = \frac{12}{50} \]
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Selecting a romance novel second (after one historical fiction book has been removed):
- After selecting one historical fiction book, there are now 49 books left on the shelf, and the number of romance novels remains at 8.
- The probability of selecting a romance novel second is: \[ P(\text{Romance second | Historical Fiction first}) = \frac{8}{49} \]
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Calculating the combined probability:
- To find the combined probability of both events occurring (selecting a historical fiction book first and then a romance novel), we multiply the two probabilities: \[ P(\text{Historical Fiction first and Romance second}) = \frac{12}{50} \times \frac{8}{49} \]
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Calculating the values:
- Now we can calculate this product: \[ P = \frac{12 \times 8}{50 \times 49} = \frac{96}{2450} \]
Thus, the final probability of selecting a historical fiction book first and then a romance novel second is: \[ \frac{96}{2450} \]
Considering the provided options, it seems there is no direct match using the fractions shown, but the calculations have been illustrated accurately. If approximations were required, it's worth analyzing which corresponds more closely or rounding those options.
If the question involves evaluating similar steps rather than exact options, ensure clarity on your selections among the formulas indicated. The most relevant framing matches thus prepares selections: \(\frac{12}{50} \times \frac{8}{49}\) is critical to highlight below as \(\frac{96}{2450}\).
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