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?\n0.114\n0.131\n0.686\n0.784
Answer
Explanation:
Step1: Calculate total number of books
The total number of books is (10 + 8=18) books.
Step2: Calculate probability of first - fiction book
The probability of choosing a fiction book first is (\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. The probability of choosing a non - fiction book second is (\frac{10}{17}) since there are 10 non - fiction books out of the remaining 17 books.
Step4: Calculate probability of third - fiction book
After choosing a fiction book first and a non - fiction book second, there are 16 books left. The probability of choosing a fiction book third is (\frac{7}{16}) since there are 7 fiction books left out of 16 remaining books.
Step5: Calculate overall probability
The overall probability of the sequence is the product of the individual probabilities: (P=\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