Question

There are 50 books on a shelf. They include 15 mystery novels, 12 works of historical fictions, 8 romance novels, and 15 nonfiction books. If Fred randomly selects 2 books from the shelf, what is the probability of selecting a historical fiction book on the first selecting and selecting romance on the second selection? Assume the books are taken without replacement. (7 points)
Responses

1250×850
12 over 50 times 8 over 50

1250×849
12 over 50 times 8 over 49

1250
12 over 50

850
8 over 50

Answer 1

To find the probability of selecting a historical fiction book first and then a romance novel second (without replacement), we can break it down into two parts.

1. **Selecting a Historical Fiction Book (First Selection)**:
- There are 12 historical fiction books out of a total of 50 books.
- The probability of selecting a historical fiction book first is:
\[
P(\text{Historical Fiction First}) = \frac{12}{50}
\]

2. **Selecting a Romance Novel (Second Selection)**:
- After selecting one book (a historical fiction), there are now 49 books left on the shelf.
- There are still 8 romance novels, so the probability of selecting a romance novel second, after having taken a historical fiction book, is:
\[
P(\text{Romance Second | Historical Fiction First}) = \frac{8}{49}
\]

3. **Calculating the Combined Probability**:
- The combined probability of both events happening (selecting a historical fiction book first, and a romance novel second) is:
\[
P(\text{Historical Fiction First and Romance Second}) = P(\text{Historical Fiction First}) \times P(\text{Romance Second | Historical Fiction First})
\]
\[
= \frac{12}{50} \times \frac{8}{49}
\]

4. **Final Calculation**:
- This simplifies to:
\[
= \frac{12 \times 8}{50 \times 49} = \frac{96}{2450}
\]

Thus, the correct expression based on the choices provided is:
\[
\frac{12}{50} \times \frac{8}{49}
\]

This corresponds to the option:
**1250×849: \(\frac{12}{50} \times \frac{8}{49}\)**.