Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Out of 100 students; 15 passed in English, 12 passed in Mathematics, 8 in Science, 6 in English and Mathematics, 7 in Mathematics and Science; 4 in English and Science; 4 in all the three. Find how many passed (i) in English and Mathematics but not in

Out of 100 students; 15 passed in English, 12 passed in Mathematics, 8 in Science, 6 in English and Mathematics, 7 in Mathematics and Science; 4 in English and Science; 4 in all the three. Find how many passed
(i) in English and Mathematics but not in Science
(ii) in Mathematics and Science but not in English
(iii) in Mathematics only
(iv) in more than one subject only

Answers (1)

Let the set of students who passed in mathematics be M, the set of students who passed in English be E and set of students who passed in science be S.

Then n(U)=100, n(M)=12, n(S)=8,

n(E\cap M)=6, n(M\cap S)=7, n(E\cap S)=4 and n(E\cap M\cap S)=4

According to the Venn diagram 
n(E\cap M\cap S)=4; e = 4

n(E\cap M)=6; d + e= 6; d = 2

n(M\cap S)=7; e + f= 7; f = 3

n(E\cap S)=4; b + e= 4; b= 0

n(E)=15; a + b + d + e= 15; a= 9

n(M)=12; d + e + f+g= 12; g= 3

n(S)=8; b + e + f + c= 8; c= 1

Thus, number of students who passed in English and mathematics but not in science = d= 2
Number of students who passed in Science  and mathematics but not in English = f=3
Number of students who passed in mathematics only = g =3 
Number of students who passed in more than one subject = b+ e+ d +f =0+4+2+3 =9
 

Posted by

infoexpert22

View full answer

Similar Questions

Latest Question