Question

A fast food chain store conducted a taste survey before marketing a new hamburger. The results of the survey showed that 75% of the people who tried this hamburger liked it. Encouraged by this result, the company decided to market the new hamburger. On a certain day, eight customers bought it for the first time. Find the probability that at least six of the eight customers will like this hamburger

Answer 1

This is a binomial distribution with n=8, p=0.75.

$P(X\ge6)=P(X=6)+P(X=7)+P(X=8)=$

$=C_8^60.75^60.25^2+C_8^70.75^70.25^1+C_8^80.75^80.25^0=0.1445.$