Given
defect rate = 3%
Number of items chosen at random = 6
Find
probability that at least one will have a defect
Explanation
Probability of defective items = 3% = 0.03
Probability of non defective items = 1 - 0.03 = 0.97
so ,
probability that at least one will have a defect = 1 - Probability of 0 defects
[tex]\begin{gathered} 1-^6C_0\times(0.03)^0(0.97)^6 \\ 1-(1\times1\times0.83297200492) \\ 1-0.83297200492 \\ 0.16702799508\approx0.167 \\ \end{gathered}[/tex]Final Answer
Hence , the probability that at least one will have a defect is 0.167(approx)
