JEE Main & Advanced Mathematics Probability Question Bank Mock Test - Probability

  • question_answer
    In a n-sided regular polygon, the probability that the two diagonal chosen at random will intersect inside the polygon is

    A) \[\frac{2{}^{n}{{C}_{2}}}{{}^{({}^{n}{{C}_{2}}-n)}{{C}_{2}}}\]

    B) \[\frac{^{n(n-1)}{{C}_{2}}}{{}^{({}^{n}{{C}_{2}}-n)}{{C}_{2}}}\]

    C) \[\frac{^{n}{{C}_{4}}}{{}^{({}^{n}{{C}_{2}}-\,n)}{{C}_{2}}}\]    

    D) none of these

    Correct Answer: C

    Solution :

    [c] When 4 points are selected, we get one intersecting point. So , probability is \[\frac{^{n}{{C}_{4}}}{^{{{(}^{n}}{{C}_{2}}-n)}{{C}_{2}}}\]


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