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

$P(X=2)=\large\frac{e^{-2}2^2}{2!}$

$\qquad\qquad=2\times 0.1353$

$\qquad\qquad=0.2706$