# Elementary Statistics

A machine has 7 identical components which function independently. The probability that a component will fail is .2. The machine will stop working if more than three components fail. Find the probability that the machine will be working?

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1. The machine will be working if
1. no part fails ---> (.8)^7
2. 1 part fails ----> C(7,1)(.2)(.8)^6
3. 2 parts fail ---> C(7,2)(.2^2)(.8^5)
4. 3 parts fail ---> C(7,3)(.2^3)(.8^4)

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2. .966

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