The defect rate of the machine is 8%.
The number of items that are chosen is 6.
To find the probability that at least one will have a defect can be calculated by the formula:
[tex]P(x)=\frac{n!}{x!(n-x)!}p^xq^{n-x}[/tex]
Where n is the number of trials (6)
x is the number of successes desired (1)
p is the probability of getting a success in one trial (8%=0.08)
q=1-p is the probability of getting a failure in one trial (1-0.08=0.92)
By replacing these values you will find the probability:
[tex]\begin{gathered} P(1)=\frac{6!}{1!(6-1)!}0.08^10.92^{6-1} \\ P(1)=6\times0.08\times0.6591 \\ P(1)=0.3164 \end{gathered}[/tex]
Then, the probability that at least one item will have a defect is 0.3164.
