Question

nadia’s bookshelf contains 10 fiction books, two reference books, and five nonfiction books. what is the probability that she randomly picks up a reference book and then, without replacing it, picks up a nonfiction book? \\(\frac{1}{289}\\) \\(\frac{10}{289}\\) \\(\frac{5}{136}\\) \\(\frac{1}{10}\\)

Explanation:

Step1: Calculate total number of books

Total books = 10 (fiction) + 2 (reference) + 5 (nonfiction) = 17.

Step2: Probability of picking reference book first

Probability (reference) = $\frac{2}{17}$ (since 2 reference books out of 17 total).

Step3: Probability of picking nonfiction book next (without replacement)

After picking a reference book, total books left = 16, nonfiction books = 5. So probability (nonfiction after reference) = $\frac{5}{16}$.

Step4: Multiply the two probabilities

Combined probability = $\frac{2}{17} \times \frac{5}{16} = \frac{10}{272} = \frac{5}{136}$.

Answer:

$\frac{5}{136}$ (corresponding to the option $\frac{5}{136}$)