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 1/10 5/136 10/289

Explanation:

Step1: Calculate total number of books

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

Step2: Probability of picking a reference book first

Number of reference books \(n(R)=2\). Probability \(P(R)=\frac{2}{17}\).

Step3: Probability of picking a non - fiction book second (without replacement)

After picking a reference book, total books left \(=16\). Number of non - fiction books \(n(NF) = 5\). Probability \(P(NF)=\frac{5}{16}\).

Step4: Use the multiplication rule for dependent events

\(P(R\text{ then }NF)=P(R)\times P(NF)=\frac{2}{17}\times\frac{5}{16}=\frac{10}{272}=\frac{5}{136}\)

Answer:

\(\frac{5}{136}\)