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Venn diagram (1 Viewer)

kpad5991

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In a class of 25 students, all of the students played at least one of the sports basketball, cricket and football. 2 of the students played all three sports. Of the 12 students who played football, 2 of them played neither of the other two sports. 9 students played football and cricket. Of the students who didn't play football 9 played cricket and 9 played basketball.

a) Draw a Venn diagram
b) How many students played only basketball out of these three sports?
 

Roy G Biv

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Working our way through the question systematically:
In a class of 25 students, all of the students played at least one of the sports basketball, cricket and football.
1. ok, total = 25, no one is outside the circles.
2 of the students played all three sports.
2. smack bang in the middle, part of all 3 circles: 2
Of the 12 students who played football, 2 of them played neither of the other two sports.
3. 2 play football only. Keep the "12" in mind for next couple of steps:
9 students played football and cricket.
4. Since 9 play football and cricket, and we've already counted 2 who play all 3 sports (from step 2), the ones who play football and cricket but not basketball must be 7.
5. Therefore, since total for football is 12, the ones who play football and basketball but not cricket must be 1.
Of the students who didn't play football 9 played cricket and 9 played basketball.
6. since 12 play football, the students who didn't play football at all (ie cricket and/or basketball only) must be 13 (since total is 25).
7. trying a few numbers (trial and error), we see that 5 must play both basketball and cricket, and 4 play basketball only, and 4 play cricket only.

a) if you follow above logic, the venn diagram should be easy to draw.
b) only basketball = 4.
 

Roy G Biv

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ok, step 7 was bugging me last night as I was trying to sleep - trial and error was wrong there.

since 9 played cricket and 9 played basketball, and 13 all up, we see that 9+9 = 18 - but it can't be 18 because there should be 13. 18-13 = 5, which is the overlapping number between those 2 circles. if it's 5 in the middle, then 9 - 5 = 4 for people playing ONLY cricket and ONLY basketball.

let me know if you can't draw the diagram, happy to draw it up for you. i did a quick diagram in paint to think through it myself - which is the point of the venn diagram.
 

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