Answer: 0.8021
Step-by-step explanation:
The given problem is a binomial distribution problem, where
[tex]n=14,\ p=0.2, q=1-0.2=0.8[/tex]
The formula of binomial distribution is :-
[tex]P(X=r)=^{n}C_{r}p^{r}q^{n-r}[/tex]
The probability that the lot will fail inspection is given by :_
[tex]P(X\geq2)=1-(P(X\leq1))\\\\=1-(P(0)+P(1))\\\\[/tex]
[tex]=1-(^{14}C_{0}(0.2)^{0}(0.8)^{14-0}+^{14}C_{1}(0.2)^{1}(0.8)^{14-1})\\\\=1-((1)(0.8)^{14}+(14)(0.2)(0.8)^{13})\\\\=0.802087907\approx0.8021[/tex]
Hence, the required probability = 0.4365
