To find the probability of selecting a historical fiction book first and a romance novel second, we can break down the problem step by step.
-
Probability of selecting a historical fiction book first:
- There are 12 historical fiction books out of a total of 50 books.
- The probability \( P(HF) \) is given by: \[ P(HF) = \frac{12}{50} \]
-
Probability of selecting a romance novel second (after selecting a historical fiction book):
- After selecting one historical fiction book, there are now 49 books left on the shelf.
- There are still 8 romance novels left.
- The probability \( P(R | HF) \) of selecting a romance novel after already having selected a historical fiction book is given by: \[ P(R | HF) = \frac{8}{49} \]
-
Combine the probabilities:
- The total probability \( P(HF \text{ and } R) \) is calculated using the multiplication rule for independent events: \[ P(HF \text{ and } R) = P(HF) \times P(R | HF) \]
Plugging in the probabilities: \[ P(HF \text{ and } R) = \frac{12}{50} \times \frac{8}{49} \]
-
Final Probability Calculation: \[ P(HF \text{ and } R) = \frac{12 \times 8}{50 \times 49} = \frac{96}{2450} \]
Thus, the final answer for the probability of selecting a historical fiction book first and a romance book second is:
\[ \frac{12}{50} \times \frac{8}{49} \]
From your provided responses, the correct expression for the probability is:
\[ \frac{12}{50} \times \frac{8}{49} \]