Question

A manufacturing machine has a 3% defect rate.If 6 items are chosen at random, what is the probability that at least one will have a defect?

Answer 1

Given

defect rate = 3%

Number of items chosen at random = 6

Find

probability that at least one will have a defect

Step-by-step 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

`\begin{gathered} 1-^6C_0*(0.03)^0(0.97)^6 \\ 1-(1*1*0.83297200492) \\ 1-0.83297200492 \\ 0.16702799508\approx0.167 \\ \end{gathered}`

Final Answer

Hence , the probability that at least one will have a defect is 0.167(approx)