Question

A study reports that 5% of adults are afraid to be home alone at night. If 20 people are randomly selected, what is the probability at least 3 of them are afraid to be home alone at night?

Answer 1

This is binomial distribution

p=0.05

q=1-0.05=0.95

$P(X \ge 3)=1-P(0)-P(1)-P(2)$

$P(0)=C^0_{20}0.05^00.95^{20}=0.358$

$P(1)=C^1_{20}0.05^10.95^{19}=0.019$

$P(2)=C^2_{20}0.05^20.95^{18}=0.189$

$P(X \ge 3)=1-0.358-0.019-0.189=0.434$