Question

a librarian has 10 nonfiction and eight fiction books from which to choose the next three book club selections. what is the approximate probability that she chooses a fiction book, then a nonfiction book, then a fiction book? 0.114 0.131 0.686 0.784

Explanation:

Step1: Calculate total number of books

Total number of books \(n = 10+8=18\)

Step2: Calculate probability of first - fiction book

Probability of choosing a fiction book first \(P(F_1)=\frac{8}{18}\)

Step3: Calculate probability of second - non - fiction book

After choosing a fiction book, number of books left \(n_1 = 17\). Probability of choosing a non - fiction book second \(P(N)=\frac{10}{17}\)

Step4: Calculate probability of third - fiction book

After choosing a fiction and a non - fiction book, number of books left \(n_2=16\). Probability of choosing a fiction book third \(P(F_2)=\frac{7}{16}\)

Step5: Calculate the combined probability

Using the multiplication rule for dependent events \(P = P(F_1)\times P(N)\times P(F_2)\)

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Answer:

0.114