Question

$10\%$ of the tools produced by a machine are defective. Find the probability distribution of the number of defective tools when $3$ tools are drawn one by one with replacement.

Answer 1

$X$ denote the no of defective machines.

$X=0$

$P\left(X\right)=(0.9{)}^3$

$X=1$

$P\left(X\right)=(0.9{)}^2\times (0.1)\times \frac{3!}{2!}$

$X=2$

$P\left(X\right)=\left(0.9\right)\times (0.1{)}^2\times \frac{3!}{1!\times 2!}$

$X=3$

$P\left(X\right)=(0.1{)}^3$