Question

A manufacturing machine has a 10% defect rate.If 4 items are chosen at random, what is the probability that at least one will have a defect? Round your answer to three decimal places.

Answer 1

Step 1

Step2

The probability that at least one will have a defect

= 1 - the probability that noon will have a defect

Step 3

Use the binomial distribution

`\begin{gathered} =1\text{ - }^nC_rp^rq^(n-r) \\ n\text{ = 4, r = 0} \\ \\ =1-^4C_0(0.1)^0(0.9)^(4-0) \\ \\ =\text{ 1 - 1}*1*0.9*0.9*0.9*0.9 \\ \\ =\text{ 0.344} \end{gathered}`