Answer to Question #154865 in Statistics and Probability for Pavan

Question

the probability of a particular type of genetic code in human species is 9/25 in a random sampling of a human species what is the probability that at least 6 has that particular type of genetic code

Answer 1

 The random variable has binomial distribution with n - the size of the sample, p = 9/25 and q = 1-p=16/25.

Hence the probability that at least 6 has that particular type of genetic code in the sample of the size N is:

$P(X\ge 6) = 1-P(X<6) = 1-P(X\le5) = \\ 1 - \displaystyle\sum_{k=0}^5\dbinom{n}{k}p^k(1-p)^{n-k}=\\ 1- \displaystyle\sum_{k=0}^5\dbinom{n}{k} \bigg( \frac9{25}\bigg)^k \bigg( \frac{16}{25}\bigg)^{n-k}$