Part 1: Answer the following question:
In a survey of students about favorite sports, the results include 22 who like tennis, 25 who like football, 9 who like tennis and football, 17 who like tennis and baseball, 20 who like football and baseball, 6 who like all three sports, and 4 who like none of the sports. How many students like only tennis and football? How many students like only tennis and baseball? How many students like only baseball and football?
Part 2: Create a Venn diagram to reflect the information in the question. You will not be able to post your Venn diagram in the discussion thread itself, but you should describe your Venn diagram and be certain to address the following questions:
How can a Venn diagram help you solve the problem?
How many circles will you need in your diagram
Where will you place the students who like all 3 sports
Where will you place the students who like none of the sports?
I need some help on this. Could anyone please give me some ideas, especially for the first part.
Part 1:
To find the number of students who like only tennis and football, we need to subtract the number of students who like both tennis and football (9) and the number of students who like all three sports (6) from the total number of students who like football (25). So,
Number of students who like only tennis and football = Number of students who like football - Number of students who like both tennis and football - Number of students who like all three sports
= 25 - 9 - 6
= 10
Similarly, to find the number of students who like only tennis and baseball, we subtract the number of students who like both tennis and baseball (17) and the number of students who like all three sports (6) from the total number of students who like tennis (22). So,
Number of students who like only tennis and baseball = Number of students who like tennis - Number of students who like both tennis and baseball - Number of students who like all three sports
= 22 - 17 - 6
= -1
Since we cannot have a negative number of students, it implies that there must have been an error in the survey or the data provided.
To find the number of students who like only baseball and football, we subtract the number of students who like both baseball and football (20) and the number of students who like all three sports (6) from the total number of students who like baseball (Unknown in the given data). Without knowing the total number of students who like baseball, we cannot find the exact number of students who like only baseball and football.
Part 2:
A Venn diagram can help visualize the relationships between different categories or groups. In this case, a Venn diagram can be used to represent the overlap and non-overlap of the three sports (tennis, football, and baseball) among the students.
You will need three circles in your Venn diagram to represent the three sports. Each circle will represent one sport (tennis, football, or baseball), and the overlapping regions will represent the students who like multiple sports.
The students who like all three sports will be placed in the overlapping region where all three circles intersect.
The students who like none of the sports will be placed outside all the circles, usually in a separate region or outside the entire diagram.
Remember to label the circles and regions appropriately to represent the specific information given in the problem.