Answered

A product is made up of 20 components in a series. Ten of the components have a 1/10,000 chance of failure. Five have a 3/10,000 chance for failure. Four have a 4/10,000 chance for failure. One component has a 1/100 chance for failure. What is the overall reliability of the product?

Answer :

Answer: The overall reliability of the product is 0.0141.

Step-by-step explanation:

Since we have given that

Number of components have a 1/10000 chance of failure = 10

Number of components have a 3/10000 chance of failure = 5

Number of components have a 4/10000 chance of failure = 4

Number of component have a 1/100 chance of failure = 1

According to question, it becomes,

[tex]10\times \dfrac{1}{10000}+5\times \dfrac{3}{10000}+4\times \dfrac{4}{10000}+\dfrac{1}{100}\\\\=\dfrac{10+5\times 3+4\times 4+100}{10000}\\\\=\dfrac{10+15+16+100}{10000}\\\\=\dfrac{141}{10000}\\\\=0.0141[/tex]

Hence, the overall reliability of the product is 0.0141.

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