Step 1:
Let $X$ be random variable denoting the no of defective bolts in a sample of 10 bolts chosen at random.
Probability that a bolt is defective=0.2
$n=10$
$\therefore \lambda=np$
$\Rightarrow 10\times .2=2$
Step 2:
Using a Poisson distribution :
$X\sim P(2)$
$\Rightarrow P(X=x)=\large\frac{e^{-2}2^x}{x!}$$\qquad x=0,1,2......$
Step 3:
Probability of exactly 2 defective bolts
$P(X=2)=\large\frac{e^{-2}2^2}{2!}$
$\qquad\qquad=2\times 0.1353$
$\qquad\qquad=0.2706$