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Math Help - Determining the probability

  1. #1
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    Determining the probability

    An infinite squence of independent trails is to be performed. Each trail results in a success with probability p and a failure with probability 1-p .What is the probability that
    i) at least 1 success occurs in the first n trails;
    ii) exactly k success occur in the first n trails;
    iii) all trails result in success ?
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  2. #2
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    Quote Originally Posted by zorro View Post
    An infinite squence of independent trails is to be performed. Each trail results in a success with probability p and a failure with probability 1-p .What is the probability that
    i) at least 1 success occurs in the first n trails;
    ii) exactly k success occur in the first n trails;
    iii) all trails result in success ?
    i) 1 - Pr(X = 0).

    ii) \Pr(X = k) = ^n C_k \, p^k (1 - p)^{n-k}.

    iii) \lim_{n \rightarrow \infty} p^n = 0.
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