Question

nadias 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?

1/289

10/289

5/136

1/10

Explanation:

Step1: Calculate total number of books

Total books = \(10 + 2+5=17\) books.

Step2: Probability of picking a reference book first

Probability of picking a reference book \(P(R)=\frac{2}{17}\) (since there are 2 reference books out of 17 total).

Step3: Probability of picking a non - fiction book second

After picking a reference book (without replacement), there are \(17 - 1=16\) books left. There are 5 non - fiction books. So probability of picking a non - fiction book \(P(N)=\frac{5}{16}\)

Step4: Use the multiplication rule for dependent events

The probability of both events \(P = P(R)\times P(N)\)

$$P=\frac{2}{17}\times\frac{5}{16}=\frac{10}{272}=\frac{5}{136}$$

Answer:

\(\frac{5}{136}\) (the third option)