Component fail

There is a 90 percent chance that a particular type of component will perform adequately under high-temperature conditions. If the device involved has four such components, determine the probability that the device is inoperable because precisely one of the four fails.

Correct answer:

p =  70.84 %

Step-by-step explanation:

$$\begin{gathered} p_1=0.90 \\ {C}_1(4)=\left(\genfrac{}{}{0ex}{}{4}{1}\right)=\frac{4!}{1!(4-1)!}=\frac{4}{1}=4 \\ {p}_2=\left(\genfrac{}{}{0ex}{}{4}{1}\right)\cdot p_1^{4-1}\cdot (1-p_1{)}^1=4\cdot 0.9^{4-1}\cdot (1-0.9{)}^1=\frac{729}{2500}=0.2916 \\ p=100\cdot (1-p_2)=100\cdot (1-0.2916)=70.84\% \end{gathered}$$

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