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JEE Main & Advanced Mathematics Probability Question Bank Self Evaluation Test - Probability-I

  • question_answer
    In a knock out chess tournament, eight players \[{{P}_{1}},\,\,{{P}_{2}},...{{P}_{8}}\] Participated. It is known that whenever the players \[{{P}_{i}}\] and \[{{P}_{j}}\] play, the player's \[{{P}_{i}}\] will win j if \[i<j\]. Assuming that the players are parried at random in each round, what is the probability that the players \[{{P}_{4}}\] reaches the final?

    A) 31/35

    B) 4/35

    C) 8/35

    D) None of these

    Correct Answer: B

    Solution :

    [b] Let us divide the players into two pools A and B each containing 4 players. Let \[{{P}_{4}}\] be in pool A. now \[{{P}_{4}}\] will reach the final if we fill the remaining three of pool A by any of \[{{P}_{5}},{{P}_{6}},{{P}_{7}}\,\,or\,\,{{P}_{s}}\]. \[\therefore \] Probability is \[\frac{^{4}{{C}_{3}}}{^{7}{{C}_{3}}}=\frac{4.3.2}{7.6.5}=\frac{4}{35}.\]


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