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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2006

  • question_answer
        A number is chosen at random among the first 120 natural numbers. The probability of the number chosen being a multiple of 5 or 15 is

    A)  \[\frac{1}{8}\]                                  

    B)  \[\frac{1}{5}\]

    C)  \[\frac{1}{24}\]                               

    D)  \[\frac{1}{6}\]

    Correct Answer: B

    Solution :

                    Key Idea: The number having unit digit 0 or 5 will be divisible by 5. All the numbers divisible by IS are also divisible by 5. In first 120 natural numbers total number of multiple of 5,\[n(A)=24\]and total number of multiple of 15,\[n(B)=8\]and\[n(A\cap B)=8\]. \[\therefore \] \[n(A\cup B)=n(A)+n(B)-n(A\cap B)\] \[=24+8-8=24\] \[\therefore \]Required probability\[=\frac{24}{120}=\frac{1}{5}\]


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