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?

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)