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

nadias bookshelf contains 10 fiction books, two reference books, and five non - fiction books. what is the probability that she randomly picks up a reference book and then, without replacing it, picks up a non - fiction 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 non - fiction books. what is the probability that she randomly picks up a reference book and then, without replacing it, picks up a non - fiction 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) books.

Step2: Calculate probability of picking a reference - book first

The probability of picking a reference book first is (P(\text{reference})=\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 (P(\text{non - fiction})=\frac{5}{16}) since there are 5 non - fiction books out of the remaining 16 books.

Step4: Calculate the combined probability

By the multiplication rule for dependent events (P(A\cap B)=P(A)\times P(B|A)), the probability of picking a reference book first and then a non - fiction book is (\frac{2}{17}\times\frac{5}{16}=\frac{10}{272}=\frac{5}{136}).

Answer:

(\frac{5}{136})