Step 1:

Let $X$ be the random variable denoting the number of students that pass in an exam out of a total of 6 students.

Probability that a student will pass =$\large\frac{80}{100}=$$0.8=p$

$X\sim B(6,0.8)$ and $q=1-0.8=0.2$

Step 2:

The probability distribution $X$ is given by

$P(X=x)=6C_x(0.8)^x(0.2)^{6-x}\qquad x=0,1,2......6$

Step 3:

Probability that at least 5 pass in the exam =$P(X\geq 5)=P(X=5)+P(X=6)$

$\qquad\qquad\qquad\qquad\qquad\qquad\qquad=6C_5(0.8)^5(0.2)+6C_6(0.8)^6$

$\qquad\qquad\qquad\qquad\qquad\qquad\qquad=(0.8)^5[6(0.2)+0.8]$

$\qquad\qquad\qquad\qquad\qquad\qquad\qquad=(0.8)^5\times 2$

$\qquad\qquad\qquad\qquad\qquad\qquad\qquad=0.65536$