How to work this question in mathematics. In a surrey of 290 newspaper reader 181 of them read the daily time 142 read the guardian 117 read punch and each at least one of three paper if 715 read the daily time and the guardian 60 read the daily time and punch and 54 read the guardian and punch a draw a venn diagram to illustrate this information b how many reader read 1 all three papers 2 exactly two of the paper 3 exactly one of the paper 4 the guardian only.
To solve this question in mathematics, you can use a Venn diagram to visualize the information given.
Step 1: Draw three overlapping circles to represent the three newspapers: Daily Time, Guardian, and Punch.
Step 2: Label each section of the circles with the number of readers that fall into each category. Let's go through each given piece of information:
- "In a survey of 290 newspaper readers" means that the total number of readers is 290.
- "181 of them read the Daily Time" means you need to write 181 inside the Daily Time circle.
- "142 read the Guardian" means you need to write 142 inside the Guardian circle.
- "117 read Punch" means you need to write 117 inside the Punch circle.
- "Each at least one of the three papers" means that there is an overall group that reads all three papers. To find this number, subtract the overlap from the total. Since 715 readers read Daily Time and Guardian, write 715 - 54 (which is the overlap between Daily Time, Guardian, and Punch) = 661 in the overlap between Daily Time and Guardian. Similarly, 60 readers read Daily Time and Punch, so write 60 - 54 = 6 in the overlap between Daily Time and Punch. Lastly, 54 readers read Guardian and Punch, so write 54 in the overlap between Guardian and Punch.
Step 3: Now you can determine the number of readers in each category:
- "How many readers read all three papers?" This is the overlap of all circles, so write the number in the intersection of all three circles. In this case, it is 54.
- "How many readers read exactly two of the papers?" These are the sections where only two circles overlap. Add up the numbers at each two-circle intersection. In this case, it's 661, 6, and 54. So, 661 + 6 + 54 = 721 readers.
- "How many readers read exactly one of the papers?" These are the sections that do not overlap with any other circles. Add up the numbers outside the overlaps in each circle. In this case, it's 181 (Daily Time), 142 (Guardian), and 117 (Punch). So, 181 + 142 + 117 = 440 readers.
- "How many readers read the Guardian only?" This is the number of readers in the Guardian circle minus the overlap with the other circles. In this case, it's 142 - 54 = 88 readers.
So, to summarize the answers:
1) 54 readers read all three papers.
2) 721 readers read exactly two of the papers.
3) 440 readers read exactly one of the papers.
4) 88 readers read the Guardian only.