50 students showed which of the following sports they liked; football, volleyball and hockey. 24 liked football, 21 volleyball and 18 hockey. 9 liked football only, 3 volleyball only and 2 hockey only. 5 liked all three sports but 6 liked football and volleyball only. Draw a venn diagram to illustrate this information. use your diagram to find the number of students who liked; exactly two sports and none of the three sports.
Please help me to solve the question i just posted
If you draw the Venn diagram, it should be clear how many like which sports and combinations. Where do you get stuck?
I stucked at where is talking about 9 liked football only downwards
Draw your Venn diagram with circles for
Football (F) upper left
Volleyball (V) upper right
Hockey (H) below, in the center
Now, the three portions on top should read 9, 6, 3
The center triangle reads 6
and the H only part reads 2
Since F=24, the F&V part must be 4
Since V=21, the V&H part must be 7
Now all the various sections are filled in and you can answer the questions.
Please solved that I just posted
To draw the Venn diagram, we need to represent the three sports: football, volleyball, and hockey.
First, let's add the numbers of students who liked each sport to the Venn diagram:
Football: 24 (including 9 who only liked football and 6 who liked football and volleyball)
Volleyball: 21 (including 3 who only liked volleyball and 6 who liked volleyball and football)
Hockey: 18 (including 2 who only liked hockey and 5 who liked all three sports)
Let's start with three overlapping circles representing each sport:
[Football] [Volleyball] [Hockey]
Now let's put the numbers associated with each group inside the circles:
Football: 9 6
Volleyball: 3
Hockey: 2 5
To find the number of students who liked exactly two sports, we need to look at the overlapping regions of the circles. In this case, it's the region where only two circles intersect (excluding the center region where all three circles overlap).
From the Venn diagram, we can see that the numbers inside the overlapping regions are:
Football and Volleyball: 6 (students who liked both football and volleyball only)
Football and Hockey: 5
Volleyball and Hockey: 0
Adding up these numbers, we get a total of 11 students who liked exactly two sports.
To find the number of students who liked none of the three sports, we need to look at the area outside all three circles. In this case, it's the region outside the entire Venn diagram.
Since the total number of students is 50, we can calculate the number of students who liked none of the three sports by subtracting the sum of the students who liked each individual sport, the students who liked exactly two sports, and the students who liked all three sports from the total:
Total number of students who liked none of the three sports = Total students - (Football + Volleyball + Hockey - (Football and Volleyball + Football and Hockey + Volleyball and Hockey) + All three sports)
Total number of students who liked none of the three sports = 50 - (24 + 21 + 18 - (6 + 5 + 0) + 5)
Total number of students who liked none of the three sports = 50 - (63 - 11 + 5)
Total number of students who liked none of the three sports = 50 - 57
Total number of students who liked none of the three sports = -7 (negative value)
Since we can't have a negative number of students, it seems that there might be an error in the given information or the calculations. Please double-check the data or let me know if you'd like me to assist you further with this problem.