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Math Help - group theory

  1. #1
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    group theory

    Hi guys, just a question from an old crpytography exam im having troubles with, thanks for the help=)

    Let G be a finite cyclic group and let g be a generator for G. Suppose |G|=12.

    Six elements of G are chosen at random (with replacement). (i)Find the probability that at least one is a generator.
    (ii)Show that the probability that two or more are the same is at least 0.77

    (i) P(at least 1 generator) = 1 - P(not getting a generator)
    = 1-(2/3)^6
    = 0.912

    (ii) Really need help with this thanks
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  2. #2
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    Quote Originally Posted by james12 View Post
    Hi guys, just a question from an old crpytography exam im having troubles with, thanks for the help=)

    Let G be a finite cyclic group and let g be a generator for G. Suppose |G|=12.

    Six elements of G are chosen at random (with replacement). (i)Find the probability that at least one is a generator.
    (ii)Show that the probability that two or more are the same is at least 0.77

    (i) P(at least 1 generator) = 1 - P(not getting a generator)
    = 1-(2/3)^6
    = 0.912

    (ii) Really need help with this thanks


    Well, what's the probability that all 6 elements chosen that way are different? It is

    \frac{11}{12}\cdot\frac{10}{12}\cdot\frac{9}{12}\c  dot\frac{8}{12}\cdot\frac{7}{12}=0.2228009... , so...

    Tonio
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