a librarian has 10 nonfiction and eight fiction books from which to choose the next three book club…
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
Answer
Explanation:
Step1: Calculate total number of books
Total books = 10 (non - fiction) + 8 (fiction)=18 books.
Step2: Calculate probability of first fiction book
Probability of choosing a fiction book first, $P_1=\frac{8}{18}$ since there are 8 fiction books out of 18 total books.
Step3: Calculate probability of second non - fiction book
After choosing a fiction book first, there are 17 books left. Probability of choosing a non - fiction book second, $P_2=\frac{10}{17}$.
Step4: Calculate probability of third fiction book
After choosing a fiction and a non - fiction book, there are 16 books left. Probability of choosing a fiction book third, $P_3=\frac{7}{16}$.
Step5: Calculate overall probability
The overall probability $P = P_1\times P_2\times P_3=\frac{8}{18}\times\frac{10}{17}\times\frac{7}{16}=\frac{8\times10\times7}{18\times17\times16}=\frac{560}{4896}\approx0.114$.
Answer:
0.114