Defect rate

A manufacturing machine has a 3% defect rate.

If 9 items are chosen randomly, what is the probability that at least one will have a defect?

Correct answer:

p =  0.2398

Step-by-step explanation:

$$\begin{gathered} r=3\%=\frac{3}{100}=0.03 \\ {p}_0=\left(\genfrac{}{}{0ex}{}{9}{0}\right)\cdot r^0\cdot (1-r{)}^{9-0}=(\genfrac{}{}{0ex}{}{9}{0})\cdot 0.03^0\cdot (1-0.03{)}^{9-0}=1\cdot 0.03^0\cdot 0.97^9\doteq 0.7602 \\ p=1-p_0=1-0.7602=0.2398 \end{gathered}$$

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