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JEE Main & Advanced Mathematics Probability Question Bank Self Evaluation Test - Probability-I

  • question_answer
    Let \[\omega \] be a complex cube root of unity with \[\omega \ne 1.\] A fair die is thrown three times. If \[r,{{r}_{2}}\] and \[{{r}_{3}}\] are the numbers obtained on the die, then the probability that \[{{\omega }^{{{r}_{1}}}}+{{\omega }^{{{r}_{2}}}}+{{\omega }^{{{r}_{3}}}}=0\] is

    A) 1/18

    B) 1/9

    C) 2/9

    D) 1/36

    Correct Answer: C

    Solution :

    [c] \[{{r}_{1}},{{r}_{2}},{{r}_{3}}\in \{1,2,3,4,5,6\}\] \[{{r}_{1}},{{r}_{2}},{{r}_{3}}\] and of the form \[3k,\,\,3k+1,\,\,3k+2\] Required probability \[=\frac{3!{{\times }^{2}}{{C}_{1}}{{\times }^{2}}{{C}_{1}}{{\times }^{2}}{{C}_{1}}}{6\times 6\times 6}=\frac{6\times 8}{216}=\frac{2}{9}.\]


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