Question

Suppose that one in five customers buy product Y. If four customers are chosen at random:
(i) what is the probability that none of them buy product Y?
(ii) what is the probability that at least three of them buy product Y?

Answer 1

$(i)P(x=0)=C_{0}^{4}(0.2)^{0}(0.8)^{4}=0.4096\\ (ii)P(x\geq3)=P(x=3)+P(x=4)\\ =C_{3}^{4}(0.2)^{3}(0.8)^{1}+C_{4}^{4}(0.2)^{4}(0.8)^{0}=0.0272\\$