The Director of Medical Services was on his annual visit to the ENT Hospital. While going through the out patients records he came across the following data for a particular day : "Ear consultations 45; Nose 50; Throat 70; Ear and Nose 30; Nose and Throat 20; Ear and Throat 30; Ear, Nose and Throat 10; Total patients 100." Then he came to the conclusion that the records were bogus. Was he right?

• n(A U B U C)=n(A)+n(b)+n(C)-n(A n B)-n(A n C)-n(B n C)+n(A n B n C)
  100=45+50+70-30-20-30+10
  100=175-80
  100=95
  Contradiction
• 13 years agoHelpfull: Yes(11) No(0)
• Ear 45;
  Nose 50;
  Throat 70;
  Ear and Nose 30;
  Nose and Throat 20;
  Ear and Throat 30;
  Ear, Nose and Throat 10;
  
  Total Patients = Ear + Nose + Throat - Ear&Nose - Nose&Throat - Ear&Throat + Ear&Nose&Throat
  So, Total Patients = 45+50+70-30-20-30+10 = 95
  But Total Patients = 100
  
  Hence, the results are bogus
• 13 years agoHelpfull: Yes(5) No(0)
• this can be done using venn diagram
  ear and nose=30,ear nose d throat=10,ear n throat=20,only ear=(45-(30+10+20))
  so records were bogus
  
• 13 years agoHelpfull: Yes(3) No(1)