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JEE Main & Advanced Mathematics Probability Question Bank Conditional probability bayes theorem

  • question_answer
    A bag X contains 2 white and 3 black balls and another bag Y contains 4 white and 2 black balls.  One bag is selected at random and a ball is drawn from it. Then the probability for the ball chosen be white is                                            [EAMCET 2003]

    A)                 \[\frac{2}{15}\]    

    B)                 \[\frac{7}{15}\]

    C)                 \[\frac{8}{15}\]    

    D)                 \[\frac{14}{15}\]

    Correct Answer: C

    Solution :

                      Let A be the event of selecting bag X, B be the event of selecting bag Y and E be the event of drawing a white ball, then \[P(A)=1/2,\,P(B)=1/2\], \[P(E/A)=2/5\] \[P(E/B)=4/6=2/3\]. \[P(E)=P(A)P(E/A)+P(B)P(E/B)=\frac{1}{2}\cdot \frac{2}{5}+\frac{1}{2}\cdot \frac{2}{3}=\frac{8}{15}\].


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