Sure! Let's break down the solution step-by-step:
1. Determine the total number of books:
On Nadia's bookshelf, there are:
- 10 fiction books
- 2 reference books
- 5 nonfiction books
Adding these together, the total number of books is:
[tex]\[
10 + 2 + 5 = 17
\][/tex]
2. Calculate the probability of picking a reference book first:
The number of reference books is 2 out of 17 total books. Therefore, the probability of picking a reference book first is:
[tex]\[
\frac{2}{17} \approx 0.1176
\][/tex]
3. Determine the remaining number of books after picking a reference book:
After picking one reference book, the remaining number of books is:
[tex]\[
17 - 1 = 16
\][/tex]
4. Calculate the probability of picking a nonfiction book next:
The number of nonfiction books is 5. So, out of the remaining 16 books, the probability of picking a nonfiction book is:
[tex]\[
\frac{5}{16} \approx 0.3125
\][/tex]
5. Combine the probabilities of both events:
To find the combined probability of both events happening (picking a reference book first, and then picking a nonfiction book next without replacement), we multiply the two probabilities:
[tex]\[
\frac{2}{17} \times \frac{5}{16} = \frac{2 \times 5}{17 \times 16} = \frac{10}{272}
\][/tex]
6. Simplify the fraction:
Simplifying the fraction [tex]\(\frac{10}{272}\)[/tex] gives:
[tex]\[
\frac{10}{272} = \frac{5}{136}
\][/tex]
So, the probability that Nadia randomly picks up a reference book and then, without replacing it, picks up a nonfiction book is [tex]\(\frac{5}{136}\)[/tex].
Thus, the correct answer is:
[tex]\[
\boxed{\frac{5}{136}}
\][/tex]
