JEE Main & Advanced Mathematics Probability Question Bank Binomial distribution

  • question_answer
    A die is thrown three times. Getting a 3 or a 6 is considered success. Then the probability of at least two successes is [DSSE 1981]

    A)                 \[\frac{2}{9}\]       

    B)                 \[\frac{7}{27}\]

    C)                 \[\frac{1}{27}\]    

    D)                 None of these

    Correct Answer: B

    Solution :

               Required probability\[=P\](exactly two)\[+P\](exactly three)                 \[={}^{3}{{C}_{2}}.{{\left( \frac{2}{6} \right)}^{2}}\left( \frac{4}{6} \right)+{}^{3}{{C}_{3}}{{\left( \frac{2}{6} \right)}^{3}}=\frac{2}{9}+\frac{1}{27}=\frac{7}{27}\].


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