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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 22

  • question_answer
    A locker can be opened by dialing a fixed three digit code (between 000 and 999). A stranger who does not know the code tries to open the locker by dialing three digits at random. The probability that the stranger succeeds at the Kth trial is A locker can be opened by dialing

    A) \[\frac{k}{999}\]        

    B)   \[\frac{k}{1000}\]

    C) \[\frac{k-1}{1000}\]   

    D)   None of these

    Correct Answer: B

    Solution :

    Let A denote the event that the stranger succeeds at the \[{{k}^{th}}\] trial. Then \[P(A')=\frac{999}{1000}\times \frac{998}{999}\,\,\times .....\times \] \[\frac{1000-k+1}{1000-k+2}\times \frac{1000-k}{1000-k+1}\] \[\Rightarrow \,\,\,P(A')=\frac{1000-k}{1000}\Rightarrow P(A)=1-\frac{1000-k}{1000}=\frac{k}{1000}\]


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