a) In a survey of youths, it was found that 85% liked to do something in their village, 60% liked to go to foreign employment. If 5% of them did not like both of them, find: 1. The percent of youths who like to do something in their village only. II. The percent of youths who like foreign employment only. III. Draw a Venn-diagram to illustrate the above information.
Answers
Let M, P and C denote the students studying Mathematics, Physics and Chemistry
And U represents total students
So, n(U)=200,
n(M)=120,n(P)=90
n(C)=70,n(M∩P)=40,n(P∩C)=30
n(M∩C)=50,n(M∪P∪C)
′
=20
∴n(M∪P∪C)
′
=n(U)−n(M∪P∪C)
⇒20=200−n(M∪P∪C)
⇒n(M∪P∪C)=180
⇒n(M∪P∪C)=n(M)+n(P)+n(C)
−n(M∩P)−n(P∩C)−n(C∩M)+n(C∩M∩P)
∴180=120+90+70−40−30−50+n(C∩M∩P)
⇒180=280−120+n(C∩M∩P)
⇒n(P∩C∩M)=300−280=20
Hence, the number of students studying all three subjects is 20.
Answer:
In a survey of a school, 300 students favour to play volleyball, 250 favour to play cricket and 110 favour both of the games. Draw a Venn-diagram and calculate:a. the number of students who play cricket only.
b. the number of students who play either volleyball or cricket.
In a survey, after their SEE, 190 students wanted to be an engineer, 160 wanted to be a doctor and 120 wanted to be both. If 300 students were interviewed, draw a Venn-diagram and find the number of students who wanted to be neither of them.