A library administrator tracked a sample of 120 books checked out last week, categorizing … — SAT

A library administrator tracked a sample of $120$ books checked out last week, categorizing them by genre (fiction or nonfiction) and format (print or audiobook). The results are summarized in the table below.

Format	Fiction	Nonfiction
Print	$45$	$35$
Audiobook	$15$	$25$

Of the books in the sample that were checked out as audiobooks, what fraction were fiction?

Cevap: 0.375

Cevap

The fraction of audiobooks that were fiction is 3/8 (which can also be gridded as the decimal .375).

To find the fraction of audiobooks that were fiction, find the total number of audiobooks in the sample by adding the values in the audiobook row:

15 + 25 = 40

. Next, find the number of fiction audiobooks, which is

15

. The fraction of audiobooks that were fiction is the ratio of these two values:

\frac{15}{40}

, which simplifies to

\frac{3}{8}

(or

0.375

in decimal form).

Adım Adım Çözüm

Calculate the total number of audiobooks in the sample.

The total number of audiobooks is

15 + 25 = 40

The question asks for the fraction of books *that were checked out as audiobooks*, which means the denominator of our fraction must be the total number of audiobooks.

Identify the number of fiction audiobooks in the sample.

There are

15

fiction audiobooks.

The question asks what fraction of the audiobooks were *fiction*, so the numerator must be the number of books that are both audiobooks and fiction.

Write and simplify the fraction representing the conditional probability.

\frac{15}{40} = \frac{3}{8}

Divide the target number of books (15) by the total number of audiobooks (40). Simplify by dividing the numerator and the denominator by their greatest common divisor, which is 5.

Anahtar Kavram

Conditional Probability from a Two-Way Table

Tahmini Süre:1m 15s

Soru

Cevap

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