JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2006

  • question_answer
        A four-digit number is formed by the digits 1, 2, 3, 4 with no repetition. The probability that the number is odd, is

    A)  zero                                     

    B)  1/3

    C)  1/4                                       

    D)  none of these

    Correct Answer: D

    Solution :

                    Key Idea: Any number is odd, if its units place is not 0, 2, 4, 6, 8. Given numbers are 1, 2, 3, 4 . Possible digits of unit digit of odd number is (either 1 or 3) = 2 Possibilities for tens digit = 3 Possibilities for hundred place digit = 2 Possibilities for thousand place digit = 1 \[\therefore \]Number of favorable outcomes \[=2\times 2\times 2\times 1=12\] Number of numbers formed by 1, 2, 3, 4 (without repetitions) = 41 \[\therefore \]Required probability\[=\frac{12}{4\times 3\times 2}=\frac{1}{2}\]


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