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QuestionA survey of 89 students found 30 use news websites, 43 use social media, and 19 use both. Find the counts for each region in a Venn diagram. How many got news from only websites? (n(n( News websites only )=11)=11) How many from only social media? (n(n( Social media only )=24)=24) How many from either? (n(n( News websites or Social media )=)=)

Studdy Solution

STEP 1

Assumptions1. The total number of students surveyed is89. . The number of students who got the news from news websites is30.
3. The number of students who got the news from social media is43.
4. The number of students who got the news from both news websites and social media is19.

STEP 2

First, we need to find the number of students who got the news from only news websites. This can be done by subtracting the number of students who got the news from both news websites and social media from the total number of students who got the news from news websites.
n(News websites only)=n(News websites)−n(Both)n(\text{News websites only}) = n(\text{News websites}) - n(\text{Both})

STEP 3

Plug in the given values for the number of students who got the news from news websites and both to calculate the number of students who got the news from only news websites.
n(News websites only)=30−19n(\text{News websites only}) =30 -19

STEP 4

Calculate the number of students who got the news from only news websites.
n(News websites only)=30−19=11n(\text{News websites only}) =30 -19 =11

STEP 5

Next, we need to find the number of students who got the news from only social media. This can be done by subtracting the number of students who got the news from both news websites and social media from the total number of students who got the news from social media.
n(Social media only)=n(Social media)−n(Both)n(\text{Social media only}) = n(\text{Social media}) - n(\text{Both})

STEP 6

Plug in the given values for the number of students who got the news from social media and both to calculate the number of students who got the news from only social media.
n(Social media only)=43−19n(\text{Social media only}) =43 -19

STEP 7

Calculate the number of students who got the news from only social media.
n(Social media only)=43−19=24n(\text{Social media only}) =43 -19 =24

STEP 8

Finally, we need to find the number of students who got the news from either news websites or social media. This can be done by adding the number of students who got the news from only news websites, only social media, and both.
n(News websites or Social media)=n(News websites only)+n(Social media only)+n(Both)n(\text{News websites or Social media}) = n(\text{News websites only}) + n(\text{Social media only}) + n(\text{Both})

STEP 9

Plug in the calculated values for the number of students who got the news from only news websites, only social media, and both to calculate the number of students who got the news from either news websites or social media.
n(News websites or Social media)=11+24+19n(\text{News websites or Social media}) =11 +24 +19

STEP 10

Calculate the number of students who got the news from either news websites or social media.
n(News websites or Social media)=+24+19=54n(\text{News websites or Social media}) = +24 +19 =54The number of students who got the news from either news websites or social media is54.

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