# Math Help - Determining the probability

1. ## 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 ?

2. Originally Posted by zorro
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) $\lim_{n \rightarrow \infty} p^n = 0$.