SOLUTION: for a military mission, engineers are creating an expensive system that relies on an important component. This component is very delicate and fragile has a probability of failure

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Question 1161231: for a military mission, engineers are creating an expensive system that relies on an important component. This component is very delicate and fragile has a probability of failure of 0.32. they install 6 of these components in parallel, in such a way that they work independently. If any one of these components works, the system works.
a) what is the probability exactly 1 of these components works?
b) what is the probability at least 1 of these components works?
Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
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Use the binomial probability distribution to solve this problem. 

(a)  P = C%5B6%5D%5E1%2A%281-0.32%29%5E1%2A0.32%5E%286-1%29 = 6%2A0.68%2A0.32%5E5 = 0.01369.    ANSWER


(b)  P = 1 - 0.32%5E6 = 1 - 0.998926.      ANSWER

Solved.