JEE Main & Advanced Mathematics Question Bank Critical Thinking

  • question_answer
    An unbiased die with faces marked 1, 2, 3, 4, 5 and 6 is rolled four times. Out of four face values obtained the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5, is [IIT 1993; DCE 2000; Roorkee 2000]

    A)                 16/81     

    B)                 1/81

    C)                 80/81     

    D)                 65/81

    Correct Answer: A

    Solution :

               \[P(\]Minimum face value not less than 2 and maximum face value is not greater than 5)            \[=P(2\,\text{or}\,3\,\text{or}\,4\,\text{or}5)=\frac{4}{6}=\frac{2}{3}\]                 Hence required probability \[={}^{4}{{C}_{4}}{{\left( \frac{2}{3} \right)}^{4}}{{\left( \frac{1}{3} \right)}^{0}}=\frac{16}{81}.\]


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