JEE Main & Advanced Mathematics Probability Question Bank Binomial distribution

  • question_answer
    The items produced by a firm are supposed to contain 5% defective items. The probability that a sample of 8 items will contain less than 2 defective items, is  [MP PET 1993]

    A)                 \[\frac{27}{20}\,{{\left( \frac{19}{20} \right)}^{7}}\]  

    B)                 \[\frac{533}{400}\,{{\left( \frac{19}{20} \right)}^{6}}\]

    C)                 \[\frac{153}{20}\,{{\left( \frac{1}{20} \right)}^{7}}\]  

    D)                 \[\frac{35}{16}\,{{\left( \frac{1}{20} \right)}^{6}}\]

    Correct Answer: A

    Solution :

               Required probability                 \[={}^{8}{{C}_{1}}{{\left( \frac{1}{20} \right)}^{1}}{{\left( \frac{19}{20} \right)}^{7}}+{}^{8}{{C}_{0}}{{\left( \frac{1}{20} \right)}^{0}}{{\left( \frac{19}{20} \right)}^{8}}=\frac{27}{20}{{\left( \frac{19}{20} \right)}^{7}}\]


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