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JEE Main & Advanced JEE Main Paper (Held On 10-Jan-2019 Evening)

  • question_answer
    If the probability of hitting a target by a shooter, in any shot, is \[\frac{1}{3}\], then the minimum number of independent shots at the target required by him so that the probability of hitting the target at least once is greater than \[\frac{5}{6}\], is- [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

    A) 4                                             

    B) 6      

    C) 5                     

    D)                  3

    Correct Answer: C

    Solution :

    \[1-{{\left( \frac{2}{3} \right)}^{n}}\,>\,\,\frac{5}{6}\] \[\Rightarrow \,\,\,\frac{1}{6}>{{\left( \frac{2}{3} \right)}^{n}}\,\] \[\Rightarrow \,\,\,{{3}^{n}}>{{2}^{n}}\times 6\] \[\Rightarrow \,\,\,{{3}^{n-1}}>{{2}^{n+1}}\] \[n=5\] (minimum)


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