Question:
To a survey of 290 newspaper readers, 181 of them read the Daily Times, 142 Read the Guardian 117 read punch and each reads at least one of the three papers if 75 read the Daily Times, and the Guardian, 60 read the Daily Times and punch, and 54 read the Guardian and punch : Draw a Venn diagram to illustrate this information How many readers read All three papers ,Exactly two of the papers The Guardian alone?
Answer:
39 read all three news papers,72 Exactly two Papers & 52 reads Guardian Alone
Step-by-step explanation:
We have given, A survey of 290 newspaper readers.
Who read the Daily times A=181
Who read the Guardian times B=142
Who read the punch C=117
Who read Daily Times and the Guardian A\cap B= 75
Who read Daily Times and the punch A\cap C=60
Who read Guardian and punch B\cap C=54
To find :
How many readers read All three papers, Exactly two of the papers The Guardian alone?
Solution :
Readers read all three papers is [tex]A\cap B\cap C[/tex]
Total survey is given by,
Total = [tex]A+B + C- A\cap B- A\cap C - B\cap C+ A\cap B\cap C[/tex]
290 = [tex]181 + 142 + 117 - 75 -60 - 54 +A\cap B\cap C[/tex]
290 =[tex]251+A\cap B\cap C[/tex]
290-251=[tex]A\cap B\cap C[/tex]
[tex]A\cap B\cap C=39[/tex]
So, number of readers who read all three papers is 39.
Exactly two of the papers = 36 + 21 + 15 = 72
Guardian Alone = 52
