In a class 40 students,31 play football,26play hockey and 13play volleyball.19 play football and hockey,8play both football and volley,and 7play both hockey and volleyball. Each student plays at least one of the three games.
i. Illustrate the information on a venn diagram.
ii.how many students play all three games.
iii.number of students who play at least two games.
iv.number of students who play exactly two games.
If x play all three, then
31+26+13 - (19+8+7) + x = 40
Now find x, and your diagram is complete, so you can easily answer the other questions.
A football team won 10 matches out of the total number of maches they played if their win parcentage was 40 , then how many matches did they play in all
i. To illustrate the information on a Venn diagram, we need to consider three overlapping circles representing football, hockey, and volleyball.
- Label one circle "Football" and another circle "Hockey".
- Write "Volleyball" in the overlapping area of the other two circles, indicating that some students play both hockey and volleyball.
- Now, let's fill in the numbers given in the question:
- Write "31" in the Football circle because 31 students play football.
- Write "26" in the Hockey circle because 26 students play hockey.
- Write "13" in the Volleyball circle because 13 students play volleyball.
- Write "19" in the overlapping area between Football and Hockey because 19 students play both games.
- Write "8" in the overlapping area between Football and Volleyball because 8 students play both games.
- Write "7" in the overlapping area between Hockey and Volleyball because 7 students play both games.
ii. To determine how many students play all three games, look at the intersection of all three circles. In this case, we can see that no number is given for the area where all three circles overlap. Therefore, the answer is zero - there are no students who play all three games.
iii. To find the number of students who play at least two games, we need to add up the number of students in each of the overlapping areas and the students who play only one game. In this case, we sum up:
- The students who play both Football and Hockey (19)
- The students who play both Football and Volleyball (8)
- The students who play both Hockey and Volleyball (7)
- The students who play all three games (0)
- The students who play only one game:
- Students who play only Football (31 - 19 - 8 = 4)
- Students who play only Hockey (26 - 19 - 7 = 0)
- Students who play only Volleyball (13 - 8 - 7 = 0)
Adding these numbers together: 19 + 8 + 7 + 0 + 4 + 0 + 0 = 38.
Therefore, 38 students play at least two games.
iv. To find the number of students who play exactly two games, we need to subtract the number of students who play all three games from the number of students who play at least two games. In this case, we found that 38 students play at least two games (from part iii) and 0 students play all three games.
Thus, the number of students who play exactly two games is 38 - 0 = 38.