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13. A certain town with a population of 100,000 has 3 newspapers: I, II, and III. The proportions of townspeople who read these papers are as follows: I: 10 percent I and II: 8 percent I and II and III: 1 percent II: 30 percent I and III: 2 percent III: 5 percent II and III: 4 percent (The list tells us, for instance, that 8000 people read newspapers I and II.) Find the number of people who read only one newspaper. How many people read at least two newspapers

Answer :

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Answer:

a) the number of people who read only one newspaper is 20,000

b) number of people read at least two newspapers is 12,000

Step-by-step explanation:

Given the data in the question;

A certain town with a population of 100,000 has 3 newspapers

a)Find the number of people who read only one newspaper

From the Venn-diagram illustrating the data in the question;

Number of that read only one paper will be;

=[ ([tex]I^{}[/tex]∩ [tex]II^{c}[/tex] ∩ [tex]III^{c}[/tex]) + ( [tex]I^{c}[/tex] ∩  [tex]II^{c}[/tex] ∩ [tex]III^{c}[/tex]) + ( [tex]I^{c}[/tex] ∩  [tex]II^{c}[/tex] ∩ [tex]III^{}[/tex]) ] × 100,000

= [ 1% + 19% + 0% ] × 100,00

= 20% × 100,000

= 20,000

Therefore, the number of people who read only one newspaper is 20,000

b) How many people read at least two newspapers;

Number of people read at least two newspapers will be;

= [ ([tex]I^{}[/tex]∩ [tex]II^{}[/tex] ∩ [tex]III^{c}[/tex]) + ( [tex]I^{}[/tex] ∩  [tex]II^{c}[/tex] ∩ [tex]III^{}[/tex]) + ( [tex]I^{c}[/tex] ∩  [tex]II^{}[/tex] ∩ [tex]III^{}[/tex]) + ( [tex]I^{}[/tex] ∩  [tex]II^{}[/tex] ∩ [tex]III^{}[/tex])  ] × 100,000

= ( 7% + 1 % + 3% + 1% ) 100,000

= 12% × 100,000

= 12,000

Therefore, number of people read at least two newspapers is 12,000

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