Question

It is known that 10% of certain articles manufactured are defective. What is the probability that in a random sample of 12 such articles 9 are defective?

Answer 1

P=$\frac{10}{100}=\frac{1}{10}$ and q=1-p=$1-\frac{1}{10}=\frac{9}{10}$

n=12, r=9 and P(X=r)=$^nC_rp^rq^{n-r}$

P(X=9)=$^{12}C_9\bigg(\frac{1}{10}\bigg)^9\bigg(\frac{9}{10}\bigg)^3=\frac{12*11*100}{1*2*3}\bigg(\frac{729}{1012}\bigg)$

=$\frac{220*729}{(10)^{12}}$