Question

The number of defective units selected when five units are chosen at random from a batch of ten flash drives which contains four detective items

Answer 1

$\dbinom{10}{5}=252$

$P(X=0)=\dfrac{\dbinom{6}{5}\dbinom{4}{0}}{\dbinom{10}{5}}=\dfrac{6(1)}{252}=\dfrac{1}{42}$

$P(X=1)=\dfrac{\dbinom{6}{4}\dbinom{4}{1}}{\dbinom{10}{5}}=\dfrac{15(4)}{252}=\dfrac{5}{21}$

$P(X=2)=\dfrac{\dbinom{6}{3}\dbinom{4}{2}}{\dbinom{10}{5}}=\dfrac{20(6)}{252}=\dfrac{10}{21}$

$P(X=3)=\dfrac{\dbinom{6}{2}\dbinom{4}{3}}{\dbinom{10}{5}}=\dfrac{15(4)}{252}=\dfrac{5}{21}$

$P(X=4)=\dfrac{\dbinom{6}{1}\dbinom{4}{4}}{\dbinom{10}{5}}=\dfrac{6(1)}{252}=\dfrac{1}{42}$

$$\begin{matrix} x & 0 & 1 & 2 & 3 & 4 \\ \\ p(x) & \dfrac{1}{42} & \dfrac{5}{21} & \dfrac{10}{21} & \dfrac{5}{21} & \dfrac{1}{42} \end{matrix}$$