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In a class of 60 students, 35 like Mathematics, 30 like Physics, and 15 like both. How many students like only Mathematics?
20
25
15
35
20
To find 'only' one group, simply subtract the intersection (both) from the total count of the specific group given in the question.
Total students = 60, students who like Mathematics (M) = 35, students who like Physics (P) = 30, students who like both (M тИй P) = 15.
Only┬аMathematics=n(M)тИТn(MтИйP)
To find 'only' one group, simply subtract the intersection (both) from the total count of the specific group given in the question.
Students often subtract the intersection from the total number of students (60) instead of the total number of students who like Mathematics (35).
Identify relevant sets
We are given the set of students who like Mathematics n(M)=35 and the set of students who like both subjects n(MтИйP)=15.
n(M)=35,n(MтИйP)=15
Apply formula for exclusive set
To find students who like only Mathematics, we subtract the overlapping portion (those who also like Physics) from the total Mathematics group.
Only┬аM=n(M)тИТn(MтИйP)
Calculate the result
Substitute the given values into the formula to find the number of students.
Only┬аM=35тИТ15=20
A is correct because subtracting the 15 students who like both subjects from the 35 who like Mathematics leaves 20 students who like only Mathematics.
This concept is a precursor to the Principle of Inclusion-Exclusion, which is frequently tested in probability problems involving dependent events.