Question

$20\%$ of the bulbs produced by a machine are defective. Find the probability distribution of the number of defective bulbs when $4$ bulbs are drawn one by one with replacement.

Answer 1

$X$ denote the no of defective bulbs.

$X=0$

$P\left(X\right)=(0.8{)}^4$

$X=1$

$P\left(X\right)=(0.8{)}^3\times (0.2)\times \frac{4!}{3!}$

$X=2$

$P\left(X\right)=(0.8{)}^2\times (0.2{)}^2\times \frac{4!}{2!\times 2!}$

$X=3$

$P\left(X\right)=\left(0.8\right)\times (0.2{)}^3\times \frac{4!}{3!}$

$X=4$

$P\left(X\right)=(0.2{)}^4$