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.
you shouldn't have to wait 9 years
Part 1: To solve this question, we need to analyze the information given and calculate the number of students who like only tennis and football, only tennis and baseball, and only baseball and football.
Let's start by representing the information in a table:
Tennis Football Baseball Total
Liked 22 25 ? ?
Liked and Both 9 6 17 ?
Liked all three ? ? ? 6
Liked none ? ? ? 4
We can use this table to calculate the missing values.
First, we need to calculate the number of students who like only tennis and football. To do this, we subtract the number of students who like both tennis and football (9) from the total number of students who like tennis (22). So, 22 - 9 = 13 students like only tennis.
Next, 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) from the total number of students who like tennis (22). So, 22 - 17 = 5 students like only tennis and baseball.
Finally, to determine the number of students who like only baseball and football, we subtract the number of students who like all three sports (6) from the total number of students who like football (25). So, 25 - 6 = 19 students like only football and baseball.
Therefore, the answers are:
- The number of students who like only tennis and football: 13
- The number of students who like only tennis and baseball: 5
- The number of students who like only baseball and football: 19
Part 2: A Venn diagram is a helpful visual representation to solve this problem. Here's how you can create one and address the given questions:
1. How can a Venn diagram help you solve the problem?
A Venn diagram helps in clearly understanding the relationships between different groups of data. It visually represents the overlapping and non-overlapping regions, making it easier to calculate the desired values.
2. How many circles will you need in your diagram?
To represent the given sports (tennis, football, and baseball), you will need three circles in your Venn diagram.
3. Where will you place the students who like all 3 sports?
To represent the students who like all three sports, you would have an overlapping region in the center where the three circles intersect.
4. Where will you place the students who like none of the sports?
Outside of the circles, you can have a separate region labeled as "none of the sports" to represent the students who like none of the sports.
Remember, you won't be able to post your Venn diagram here, but you can draw one on paper or use any online Venn diagram tools to visualize the information and solve the problem more effectively.