The table below summarizes the results of a survey conducted by a market research firm. Th… — SAT

The table below summarizes the results of a survey conducted by a market research firm. The survey asked $160$ randomly selected adults about their age group and their primary source of news.

Age group	Digital/Social Media	Print/Television	Total
Under 40	$68$	$12$	$80$
40 and older	$32$	$48$	$80$
Total	$100$	$60$	$160$

Given that a randomly selected person from the survey has digital or social media as their primary news source, what is the probability that the person is under 40 years old?

A
$\frac{17}{40}$
$\frac{17}{25}$ Answer
C
$\frac{17}{20}$
D
$\frac{5}{8}$

Answer

The correct answer is

\frac{17}{25}

(representing the ratio of individuals under 40 years old among those who use digital/social media as their primary news source).

The correct answer is

\frac{17}{25}

. To find the conditional probability that a randomly selected person is under 40 years old given that their primary news source is digital or social media, the denominator must represent the total number of people who satisfy the given condition (

100

). The numerator must represent the number of people who satisfy both conditions (are under 40 years old and have digital/social media as their primary news source, which is

68

). Dividing these values yields

\frac{68}{100}

, which simplifies to

\frac{17}{25}

Step-by-Step Solution

Identify the size of the restricted sample space based on the conditional statement in the question.

The total number of surveyed individuals whose primary news source is digital or social media is

100

The phrase 'Given that a randomly selected person... has digital or social media as their primary news source' restricts the denominator to the column total for digital/social media.

Identify the number of favorable outcomes within the restricted sample space.

Within the group of

100

individuals who use digital/social media, the number of individuals who are under 40 years old is

68

This value serves as the numerator for the conditional probability.

Divide the number of favorable outcomes by the size of the restricted sample space and simplify the resulting fraction.

The probability is

\frac{68}{100} = \frac{17}{25}

Both numbers are divided by their greatest common divisor,

4

, to simplify the fraction to its lowest terms.

Key Concept

Conditional Probability in Two-Way Tables

Question

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Step-by-Step Solution

Key Concept

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