Functionality 24461

The daily product consists of 1000 components, and the probability of failure of any component during the use of the device is 0.001. It does not depend on other components. What is the probability of failure of two components in the investigated period of functionality?

Correct answer:

p =  0.184

Step-by-step explanation:

$$\begin{gathered} q=0.001 \\ {C}_2(1000)=\left(\genfrac{}{}{0ex}{}{1000}{2}\right)=\frac{1000!}{2!(1000-2)!}=\frac{1000\cdot 999}{2\cdot 1}=499500 \\ p=\left(\genfrac{}{}{0ex}{}{1000}{2}\right)\cdot q^2\cdot (1-q{)}^{1000-2}=499500\cdot 0.001^2\cdot (1-0.001{)}^{1000-2}=0.184 \end{gathered}$$

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