Machine defect probability

The machine produces one part in 2 minutes. The probability that it is defective is 0.05. What probability will the machine produce exactly ten defective parts per shift (8 hours)?

Final Answer:

p =  0.1062

Step-by-step explanation:

$$\begin{gathered} C_{10}(240)=\left(\genfrac{}{}{0ex}{}{240}{10}\right)=\frac{240!}{10!(240-10)!}=144485086176559128 \\ {t}_1=2\text{min} \\ {t}_2=8\text{h}\to \text{min}=8\cdot 60\text{min}=480\text{min} \\ q=0.05 \\ n=t_2/t_1=480/2=240 \\ p=\left(\genfrac{}{}{0ex}{}{n}{10}\right)\cdot q^{10}\cdot (1-q{)}^{n-10}=144485086176559128\cdot 0.05^{10}\cdot (1-0.05{)}^{240-10}=0.1062 \end{gathered}$$

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