Question

A company responds to 80% of all enquiries within 2 working days. The firm received 8 enquiries today. What is the probability that all the 8 enquiries are responded within 2 working days?

Answer 1

Let $X=$ the number of enquiries responded: $X\sim Bin(n, p).$

Given $p=0.8, n=8.$

$$P(X=8)=\dbinom{8}{8}(0.8)^8(1-0.8)^{8-8}=0.8^8$$

$$=0.16777216\approx0.1678$$

$0.1678$