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Answer :
The fraction of programmers who know neither FORTRAN nor COBOL is 3/10. So, fifth option is the correct answer.
To determine the fraction of programmers who know neither FORTRAN nor COBOL, we need to subtract the fractions of programmers who know FORTRAN, COBOL, and both from the total.
It is given that, 2/3 of the programmers know FORTRAN, 1/5 know COBOL, and 1/6 know both.
Fraction who know neither = 1 - (Fraction who know FORTRAN + Fraction who know COBOL - Fraction who know both)
Fraction who know neither = 1 - (2/3 + 1/5 - 1/6)
Simplifying the expression:
Fraction who know neither = 1 - (20/30 + 6/30 - 5/30)
Fraction who know neither = 1 - 21/30
Fraction who know neither = 9/30
Simplifying further by dividing both numerator and denominator by 3:
Fraction who know neither = 3/10
Therefore, the fraction of programmers who know neither FORTRAN nor COBOL is 3/10. So, fifth option is the correct answer.
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