Answer:
Step-by-step explanation:
Given
17 % of the drivers stopped have invalid licenses
n=24 drivers are stopped
using Binomial distribution
[tex]^nC_r(p)^r(q)^{n-r}[/tex]
here p=0.17
q=1-0.17=0.83
(a)none will have valid license i.e. r=0
[tex]P(r=0)^{24}C_0(0.17)^0(0.83)^{24}=(0.83)^{24}=0.0114[/tex]
(b)Exactly one have invalid license i.e. r=1
[tex]P(r=1)=^{24}C_1(0.17)^1(0.83)^{23}=24\times 0.17\times (0.83)^{23}[/tex]
[tex]=0.0561[/tex]
(c)At least 2 will have invalid license i.e. [tex]r\geq 2[/tex]
[tex]P(r\geq 2)=1-P(r=0)-P(r=1)[/tex]
[tex]P(r\geq 2)=1-0.0114-0.0561[/tex]
[tex]P(r\geq 2)=0.932[/tex]
