30% of chicken is contaminated, if a person buys 12, what's the possibility that 6 of them are contaminated? thanks
Hi
Let X be the random variable which counts the number of chickens contaminated out of 12.
X follows a binomial distribution (with parameters n=12 and p=0.30) because it is the number of "yes" in a sequence of 12 independent yes/no experiments (contaminated / not contaminated).
$\displaystyle P(X=k) = \binom{n}{k} p^k (1-p)^{n-k}$
Therefore $\displaystyle P(X=6) = \binom{12}{6} 0.30^6\: (1-0.30)^{12-6}$
$\displaystyle P(X=6) = \binom{12}{6} 0.30^6 \: 0.70^6$