Question

It has been found that one out of every four people who visit a retail website make a purchase worth R500 or more. If we randomly select a sample of 5 visitors to the website, what is the probability that less than one of the visitors will make a purchase worth R500 or more? 

Answer 1

Solution:

Let $X=$ the number of the visitors who will make a purchase worth R500 or more: $X\sim Bin(n,p)$

Given $p=1/4=0.25, n=5.$

$$P(X=x)=\dbinom{n}{x}p^x(1-p)^{n-x}$$ $$P(X<1)=P(X=0)$$ $$=\dbinom{5}{0}0.25^0(1-0.25)^{5-0}$$ $$\approx0.2373$$