Given : The probability that telephone bills mailed to house-holds in Hong Kong are incorrect.=0.01
[tex]P(x)=^nC_xp^x(1-p)^{n-x}[/tex]
If a sample of 10 bills is selected, then the probability that at least one bill will be incorrect :-
[tex]P(x\geq1)=1-P(0)\\\\=1-^{10}C_{0}(0.1)^0(0.9)^{10}\\\\=1-(0.9)^{10}=0.6513[/tex]
Hence, the probability that at least one bill will be incorrect =0.6513
[tex]P(x;\mu)=\dfrac{e^{-\mu}\mu^x}{x!}[/tex]
Mean : [tex]\mu=np=10\times0.1=1[/tex]
Then , If a sample of 10 bills is selected, then the probability that at least one bill will be incorrect :-
[tex]P(x\geq1)=1-P(0)\\\\=1-\dfrac{e^{-1}1^0}{0!}\\\\=1-0.3678=0.6321[/tex]
Hence, the probability that at least one bill will be incorrect =0.6321
