JEE Main & Advanced Mathematics Question Bank Critical Thinking

  • question_answer
    A box contains 24 identical balls, of which 12 are white and 12 are black. The balls are drawn at random from the box one at a time with replacement. The probability that a white ball is drawn for the 4th time on the 7th draw is [IIT Screening 1994]

    A)                 \[\frac{5}{64}\]    

    B)                 \[\frac{27}{32}\]

    C)                 \[\frac{5}{32}\]    

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

    Correct Answer: C

    Solution :

               To get 3 white balls in first 6 draw and then a white again in 7th draws.                 \[P={}^{6}{{C}_{3}}\times {{\left( \frac{1}{2} \right)}^{3}}\left( \frac{1}{2} \right)\text{ }\left( \frac{1}{2} \right)\Rightarrow P=\frac{5}{32}\].


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