Question

ChangeA survey of 64 college students was taken to determine where they got the news about what's qoing on in the world. Of those surveyed, 25 got the news fromnewspapers, 30 from television, and 7 from both newspapers and television. Construct a Venn diagram and determine the cardinality for each region. Use thecompleted Venn Diagram to answer the following questions. How many got the news from only newspapers?n(Newspapers only) = how many got the news from only television? N(television only) =how many got the news from newspapers or television?n(newspapers or television) =how many would not get the news from either newspapers or television? N(neither)=

Answer 1

Answer:

a) n(newpaper only) = 18

b) n(Television only) = 23

c) n(newspapers or television) = 48

d) n(neither) = 16

Step-by-step explanation:

Given:

Total students surveyed = 64

Number of students that got the news from newspaper = 25

Those that got from the television = 30

Those that got from both newspaper and television = 7

To find:

The number of students that got the news from only newspapers

We will be using Venn terms:

a) n(newspaper only) + n(newspaper n television) = Number of students that got the news from newspaper

n(newspaper n television) = 7

n(newspaper only) + 7 = 25

n(newpaper only) = 25 - 7

n(newpaper only) = 18

constructing a Venn diagram:

b) n(Television only) + n(newspaper n television) = Those that got news from the television

n(Television only) + 7 = 30

n(Television only) = 30 - 7

n(Television only) = 23

c) n(newspapers or television) = n(Television only) + n(Newspapers) + n(newspaper n television)

n(newspapers or television) = 23 + 18 + 7

n(newspapers or television) = 48

d) n(newpapaer only) + n(television) + n(newspaper n television) + n(neither) = Total students surveyed

18 + 7 + 23 + n(neither) = 64

48 + n(neither) = 64

n(neither) = 64 - 48

n(neither) = 16