Answer: [tex]\dfrac{26}{27}[/tex]
Step-by-step explanation:
Given : To avoid detection at customs, a traveler places 6 narcotic tablets in a bottle containing 9 vitamin tablets that are similar in appearance.
Proportion of success : [tex]p=\dfrac{6}{9}=\dfrac{2}{3}[/tex]
Sample size taken by customs official : n= 3
Let x be a binomial variable that represents the tablets in the bottle.
Using Binomial probability formula :-
[tex]P(X=x)=^nC_xp^x(1-p)^{n-x}[/tex]
The probability that the traveler will be arrested for illegal possession of narcotics =[tex]P(x\geq1)=1-P(x=0)[/tex]
[tex]1-^3C_0(\dfrac{2}{3})^0(1-\dfrac{2}{3})^3\\\\=1-(1)(1)(\dfrac{1}{3})^3\ [\becuase ^nC_0=1]\\\\=1-\dfrac{1}{27}=\dfrac{26}{27}[/tex]
Hence, the probability that the traveler will be arrested for illegal possession of narcotics = [tex]\dfrac{26}{27}[/tex]
