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JEE Main & Advanced Mathematics Probability Question Bank Definition of probability

  • question_answer
    A bag contains 3 white, 3 black and 2 red balls. One by one three balls are drawn without replacing them. The probability that the third ball is red, is [MNR 1994]

    A)                 \[\frac{1}{2}\]       

    B)                 \[\frac{1}{3}\]

    C)                 \[\frac{2}{3}\]       

    D)                 \[\frac{1}{4}\]

    Correct Answer: D

    Solution :

               Let R stand for drawing red ball \[B\] for drawing black ball and \[W\] for drawing white ball.            Then required probability            \[=P(WWR)+P(BBR)+P(WBR)+P(BWR)+P(WRR)+\]            \[P(BRR)+P(RWR)+P(RBR).\]            \[=\frac{3.2.2}{8.7.6}+\frac{3.2.2}{8.7.6}+\frac{3.3.2}{8.7.6}+\frac{3.3.2}{8.7.6}+\frac{3.2.1}{8.7.6}\]                                                  \[+\frac{3.2.1}{8.7.6}+\frac{2.3.1}{8.7.6}+\frac{2.3.1}{8.7.6}\] \[=\frac{2}{56}+\frac{2}{56}+\frac{3}{56}+\frac{3}{56}+\frac{1}{56}+\frac{1}{56}+\frac{1}{56}+\frac{1}{56}=\frac{1}{4}\].


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