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JEE Main & Advanced Sample Paper JEE Main Sample Paper-46

  • question_answer
    A box contains 15 transistors, 5 of which are defective. An inspectors takes out one transistor at random, examines it for defects and replaces it. After it has been replaced another inspector does the same thing and then so does a third inspector. The probability at least one of the inspectors, finds a defective transistor is equal to

    A)  1/27               

    B)  8/27              

    C)  19/27                         

    D)  26/27

    Correct Answer: C

    Solution :

     Probabiltiy of defective transistor \[=\frac{5}{15}=\frac{1}{3}\] and probability of non-defective transistor \[=1-\frac{1}{3}=\frac{2}{3}\] Probability that the inspector find a non-defective transistor \[=\,\frac{2}{3}\times \frac{2}{3}\times \frac{2}{3}=\frac{8}{27}\] Hence, probability that atleast one of d the inspectors find a defective transistors \[=1-\frac{8}{27}=\frac{19}{27}\]


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