Question

In a class test of 70 students, 23 and 30 students passed in mathematics and in statistics respectively
and 15 passed in mathematics but not passed in statistics. Using set theory result, find the number
of student who passed in both the subjects and who did not pass in both the subjects.

Answer 1

Given :   In a class test of 70 students, 23 and 30 students passed in mathematics and in statistics respectively and 15 passed in mathematics but not passed in statistics

To find :  the number of student who passed in both the subjects and who did not pass in both the subjects.

Solution:

Total Students  = 70

Passed in mathematics = 23

Failed in Mathematics = 70 - 23 = 47

Passed in Statistics  = 30

Failed in Statistics  = 70 - 30 = 40

Passed in Mathematics  but bot passes in Statistic  =  15

=> 15  = 23  - Passed in Both

=> Passes in Both  = 8

Total Passed Students  =  passed in Maths + statistics - Both

= 23 + 30 - 8

= 45

Failed in Both = Total Students - Total Passes Students

= 70 - 45

= 25

Failed in Both  = 25  

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