Answer: 0.6521
Step-by-step explanation:
According to the Binomial distribution , the provability of getting x successes in n trials is given by :-
[tex]P(x)=^nC_xp^x(1-p)^{n-x}[/tex] , where p=probability of getting success in each trial.
Let x denotes the number of defective products.
here , n=7 and p =0.14
Then, the probability that among 7 randomly selected products, at least one of them is defective= P(X ≥ 1) =1- P(X<1)
= 1- P(X=0)
[tex]=1-^7C_0(0.14)^0(1-0.14)^7[/tex]
[tex]=1-(1(1)(0.86)^7\ \[\because ^nC_0=1][/tex]
[tex]=1-0.347927822217[/tex]
[tex]=0.652072177783\approx0.6521[/tex]
Hence, the probability that among 7 randomly selected products, at least one of them is defective is 0.6521 .
