Question

A manufacturing machine has a 10% defect rate. If 8 items are chosen at random, what is the probability that at least one will have a defect?

Answer 1

The probability at least one will have a defect is 1 - the probability no one will have a defect.

The probability no one will have a defect is:

`\begin{gathered} (90)/(100)\cdot(90)/(100)\cdot(90)/(100)\cdot(90)/(100)\cdot(90)/(100)\cdot(90)/(100)\cdot(90)/(100)\cdot(90)/(100) \\ =(0.9)^8 \\ =0.4305 \end{gathered}`

So, the probability (P) that at least one will have a defect:

P = 1 - 0.4305

P = 0.5695 = 56.95%

Answer:

P = 0.5695 = 56.95%.