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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 40

  • question_answer
    A batch of 50 transistors was purchased from three different companies A, B and C. 18 of them were manufactured by A, 20 by B and the rest were manufactured by C. The companies A and C produce excellent quality transistors with probability equal to \[0.9,\] B produces the same with the probability equal to\[0.6\]. Then the probability of the event that an excellent quality transistor chosen at random is manufactured by the company B is

    A) \[4/11\]

    B)        \[3/11\]

    C)    \[4/13\]

    D)        \[3/13\]

    Correct Answer: C

    Solution :

    [c] Let A, B and C be the events that the transistor chosen is manufactured by the companies A, B and C, respectively. Let E be the event that the transistor is of excellent quality. So,   \[P(A)=\frac{18}{50};\,\,\,\,P(B)=\frac{20}{50};\,\,\,\,P(C)=\frac{12}{50}\] Also,   \[P(E/A)=0.9;\] \[P(E/B)=0.6;\] \[P(E/C)=0.9\] \[\therefore \,\,\,\,\,P(E)=P(A)\,\,P(E/A)+P(B)\,\,P(E/B)+P(C)\,\,P(E/C)\]       \[=\frac{39}{50}\] \[\therefore \]  Required probability  \[=P(B/E)\]             \[=\frac{P(B)\,P(E/B)}{P(E)}=\frac{\frac{20}{50}\times 0.6}{\frac{39}{50}}=\frac{4}{13}\]           


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