nadias bookshelf contains 10 fiction books, two reference books, and five nonfiction books. what is the…

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?\n\\(\\frac{1}{289}\\)\n\\(\\frac{10}{289}\\)\n\\(\\frac{5}{136}\\)\n\\(\\frac{1}{10}\\)

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?\n\\(\\frac{1}{289}\\)\n\\(\\frac{10}{289}\\)\n\\(\\frac{5}{136}\\)\n\\(\\frac{1}{10}\\)

Answer

Explanation:

Step1: Calculate total number of books

The total number of books is $10 + 2+5=17$.

Step2: Calculate probability of picking a reference book first

The probability of picking a reference book first is $\frac{2}{17}$ since there are 2 reference books out of 17 total books.

Step3: Calculate probability of picking a non - fiction book second

After picking a reference book without replacement, there are 16 books left. The probability of picking a non - fiction book second is $\frac{5}{16}$ since there are 5 non - fiction books out of the remaining 16 books.

Step4: Calculate the combined probability

The probability of both events happening is the product of the probabilities of each event. So $P=\frac{2}{17}\times\frac{5}{16}=\frac{10}{272}=\frac{5}{136}$.

Answer:

$\frac{5}{136}$