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JEE Main & Advanced Mathematics Probability Question Bank Self Evaluation Test - Probability-I

  • question_answer
    A certain type of missile hits the target with probability p=0.3. What is the least number of missiles should be fired so that there is at least an 80% probability that the target is hit?

    A) 5

    B) 6

    C) 7

    D) None of the above

    Correct Answer: A

    Solution :

    [a] Probability of hitting the target = 0.3 If ?n? is the no. of times that the missile is fired. \[\therefore \] Probability of hitting at least once \[=1-{{[1-0.3]}^{n}}=0.8\] \[{{0.7}^{n}}=0.2\] \[n\log 0.7=\log 0.2\] \[\Rightarrow n=4.512\] for \[n=4;\,\,p<0.8\] take n = 5 \[\] Hence 5 missiles should be fired so that there is at least 80% prob. That the target is hit.


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