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 bionomial distribution :

$n=10,p=0.2\Rightarrow q=0.8$

$X\sim B(10,0.2)$

$P(X=x)=10C_x(0.2)^x(0.8)^{10-x}\qquad x=0,1,2.......10$

Step 3:

Probability of exactly 2 defective bolts

$P(X=2)=10C_2(\large\frac{2}{10})^2(\large\frac{8}{10})^8$

$\qquad\qquad=\large\frac{10\times 9}{1\times 2}\frac{1}{5^2}\frac{4^8}{5^8}$

$\qquad\qquad=\large\frac{45}{5^{10}}$$\times 2^{16}$

$\qquad\qquad=\large\frac{45(2^{16})}{5^{10}}$