Question There are 50 books on a shelf. They include 15 mystery novels, 12 works of historical fiction, 8 romance novels, and 15 nonfiction books. If Federica randomly selects 2 books from the shelf, what is the probability of selecting a historical fiction book on the first selection and selecting romance on the second selection? Assume the books are taken without replacement.(1 point) Responses 1250⋅849 Start Fraction 12 over 50 End Fraction times Start Fraction 8 over 49 End Fraction 850 Start Fraction 8 over 50 End Fraction 1250 Start Fraction 12 over 50 End Fraction 1250⋅850 Start Fraction 12 over 50 End Fraction times Start Fraction 8 over 50 End Fraction

To find the probability of selecting a historical fiction book on the first selection and a romance novel on the second selection without replacement, we can use the following steps:

1. Calculate the probability of selecting a historical fiction book first:

   • There are 12 historical fiction books out of 50 total books.
   • So, the probability \( P(HF) \) of selecting a historical fiction book first is: \[ P(HF) = \frac{12}{50} \]

2. Calculate the probability of selecting a romance novel second:

   • After removing one historical fiction book, there are now 49 books left on the shelf.
   • There are still 8 romance novels remaining.
   • So, the probability \( P(R | HF) \) of selecting a romance novel after a historical fiction book has been selected is: \[ P(R | HF) = \frac{8}{49} \]

3. Combine the probabilities:

   • The overall probability \( P(HF \text{ and } R) \) of selecting a historical fiction book first and a romance novel second is: \[ P(HF \text{ and } R) = P(HF) \times P(R | HF) \]
   • Substituting the values we calculated: \[ P(HF \text{ and } R) = \frac{12}{50} \times \frac{8}{49} \]

4. Calculate the result: \[ P(HF \text{ and } R) = \frac{12 \times 8}{50 \times 49} = \frac{96}{2450} \]

Thus, the probability of selecting a historical fiction book first and then a romance novel second is \( \frac{96}{2450} \).

Let's examine the answers provided and see which corresponds to this result. None of the exact fractions correspond directly to this; however, if it were asking in decimal form or further simplified, we would proceed accordingly.

In a simplified form, \( \frac{96}{2450} \) can be further reduced. The greatest common divisor (GCD) of 96 and 2450 is 2: \[ \frac{96 \div 2}{2450 \div 2} = \frac{48}{1225} \]

So, it simplifies to \( \frac{48}{1225} \).

Finally, if the problem indicates needing a probability format or checking each response numerically would yield more clarity regarding correctness against provided options.

Conclusion: The exact answer for the probability of the selections in reduced fraction is \( \frac{48}{1225} \).