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JEE Main & Advanced Sample Paper JEE Main Sample Paper-32

  • question_answer
    A test is made up of 5 questions, for each question there are 4 possible answers and only one is correct. For every right choice you gain 1 mark while for each wrong choice there is a penalty of 1 mark. The probability of getting at least 2 marks answering to every question in a random way is

    A) \[\frac{1}{16}\]  

    B)                                    \[\frac{1}{64}\]

    C) \[\frac{15}{64}\]         

    D)                                    \[\frac{1}{1024}\]

    Correct Answer: B

    Solution :

    To get at least 3 marks at least 4 must be right. Now, n = 5; \[p=\frac{1}{4};q=\frac{3}{4}\] \[r=4\,or\,5\]. \[\therefore \,\,\,P(r\,\underline{>}\,4){{=}^{5}}{{C}_{4}}{{\left( \frac{1}{4} \right)}^{4}}.\left( \frac{3}{4} \right){{+}^{5}}{{C}_{5}}{{\left( \frac{1}{4} \right)}^{5}}\] \[=5.\frac{1}{256}.\frac{3}{4}+\frac{1}{45}=\frac{16}{4\times 256}=\frac{1}{64}\]


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