Question

1. a bookshelf contains 9 mysteries, 7 biographies, and 4 science fiction books. a book is randomly selected, not replaced, then another is selected. find the probability of selecting a biography then a mystery.

$\frac{63}{380}$
$\frac{16}{39}$
$\frac{9}{219}$
$\frac{7}{20}$

Explanation:

Step1: Calculate total number of books

The total number of books is $9 + 7+4=20$.

Step2: Calculate probability of first - selecting a biography

The probability of selecting a biography first is $\frac{7}{20}$ since there are 7 biographies out of 20 books.

Step3: Calculate probability of second - selecting a mystery after a biography

After one biography is selected and not replaced, there are 19 books left and 9 mysteries. So the probability of selecting a mystery second is $\frac{9}{19}$.

Step4: Calculate the combined probability

Since these are dependent events, the probability of selecting a biography then a mystery is $\frac{7}{20}\times\frac{9}{19}=\frac{63}{380}$.

Answer:

$\frac{63}{380}$