JEE Main & Advanced AIEEE Solved Paper-2009

  • question_answer In a binomial distribution \[B\left( n,p=\frac{1}{4} \right),\]if  the probability of at least one success is greater than or equal to\[\frac{9}{10}\], then n is greater than     AIEEE  Solved  Paper-2009

    A)                                                     \[\frac{1}{\log _{10}^{4}-\log _{10}^{3}}\]           

    B) \[\frac{1}{\log _{10}^{4}+\log _{10}^{3}}\]

    C)                        \[\frac{9}{\log _{10}^{4}-\log _{10}^{3}}\]           

    D) \[\frac{4}{\log _{10}^{4}-\log _{10}^{3}}\]

    Correct Answer: A

    Solution :

    \[P(x\ge 1)\ge \frac{9}{10}\] \[\Rightarrow \] \[1-P(x=0)\le \frac{9}{10}\] \[\Rightarrow \] \[\frac{1}{10}\ge {{\left( \frac{3}{4} \right)}^{n}}\] \[\Rightarrow \] \[{{\left( \frac{3}{4} \right)}^{n}}\le \frac{1}{10}\] \[\Rightarrow \] \[n[\log _{10}^{3}-\log _{10}^{4}]\le -1\] \[\Rightarrow \] \[n\ge \frac{1}{\log _{10}^{4}-\log _{10}^{3}}\]

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