2. Consider a system of five identic al components connected in series, as illustrated in the figure below. 2 3 4 5 (a) Let A be the event that the system fails. For A to occur, at le ast one of the individual components must fail. How many outcomes are in the event A? Denote a component that fails by F and one that doesn't fail by S (for success). (b) What is the probability that 3 of the 5 components fail? (c) What is the probability that component 2 and com ponnt 4 fail?

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2. Consider a system of five identic al components connected in series, as illustrated in the figure
below.
2
3
4
5
(a)
Let A be the event that the system fails. For A to occur, at le ast one of the individual
components must fail. How many outcomes are in the event A?
Denote a component that fails by F and one that doesn't fail by S (for success).
(b)
What is the probability that 3 of the 5 components fail?
(c)
What is the probability that component 2 and com ponnt 4 fail?
Transcribed Image Text:2. Consider a system of five identic al components connected in series, as illustrated in the figure below. 2 3 4 5 (a) Let A be the event that the system fails. For A to occur, at le ast one of the individual components must fail. How many outcomes are in the event A? Denote a component that fails by F and one that doesn't fail by S (for success). (b) What is the probability that 3 of the 5 components fail? (c) What is the probability that component 2 and com ponnt 4 fail?
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