Probable chances in life #4

Let $X$ be the number of defective items.

$P$ (an item is defective) = $p$ = $\dfrac{10}{100}=0.1$ ,and

$q=1-0.1=0.9$

Since $n=5$

Therefore $X\sim{B}(5,0.1)$

The probability mass function of $X$ is given as :-

$P(X=x)=p(x)=^{5}{{C}}_{x}(0.1)^{x}.(0.9)^{5-x}$ where

$x=0,1,2,3,4,5$

$P$ (atmost one defective item is received) = $P(X\le{1})$

= $P(X=0)+P(X=1)$

= $^{5}{{C}}_{0}(0.1)^{0}.(0.9)^{5}+^{5}{{C}}_{1}(0.1)^{1}.(0.9)^{4}$

= $\dfrac{9^{5}}{10^{5}}+\dfrac{5(9^{4})}{10^{5}}$

= $\dfrac{91854}{10^{5}}$

= $\boxed{0.91854}$