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JEE Main & Advanced Mathematics Probability Question Bank Binomial distribution

  • question_answer
    In a box containing 100 eggs, 10 eggs are rotten. The probability that out of a sample of 5 eggs none is rotten if the sampling is with replacement is       [MP PET 1991;             MNR 1986; RPET 1995; UPSEAT 2000]

    A)                 \[{{\left( \frac{1}{10} \right)}^{5}}\]               

    B)                 \[{{\left( \frac{1}{5} \right)}^{5}}\]

    C)                 \[{{\left( \frac{9}{5} \right)}^{5}}\] 

    D)                 \[{{\left( \frac{9}{10} \right)}^{5}}\]

    Correct Answer: D

    Solution :

               Let \[P(\text{fresh}\,\text{egg})=\frac{90}{100}=\frac{9}{10}=p\]            \[P(\text{rotten}\,\text{egg})=\frac{10}{100}=\frac{1}{10}=q\];  \[n=5,\] \[r=5\]            So the probability that none egg is rotten                                                 \[={}^{5}{{C}_{5}}{{\left( \frac{9}{10} \right)}^{5}}.{{\left( \frac{1}{10} \right)}^{0}}={{\left( \frac{9}{10} \right)}^{5}}\].


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