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A machine is made up of two components, A and B. Each compon

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A machine is made up of two components, A and B. Each compon [#permalink] New post 10 Aug 2018, 06:34
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53% (01:16) correct 46% (01:12) wrong based on 28 sessions
A machine is made up of two components, A and B. Each component either works or fails. The failure or non-failure of one component is independent of the failure or non-failure of the other component. The machine works if at least one of the components works.

If the probability that each component works is \(\frac{2}{3}\), what is the probability that the machine works?

A. \(\frac{1}{9}\)

B. \(\frac{4}{9}\)

C. \(\frac{1}{2}\)

D. \(\frac{2}{3}\)

E. \(\frac{8}{9}\)

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[Reveal] Spoiler: OA

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Re: A machine is made up of two components, A and B. Each compon [#permalink] New post 10 Aug 2018, 09:50
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I don't know if this is poor form as I just joined, so moderators please stop me if I'm doing things I shouldn't.

Explanation below:

We want to know if the machine works, or in other words if the machine doesn't fail. The only case where the machine fails is when both the components fail.

We know that each component fail independently of the other components, and as the probability that each component works is 2/3, the probability that each component fails is 1-2/3, or 1/3.

Then we can figure out the probability that the machine fails. It is the probability that the first component fails times the probability that the second component fails.

1/3*1/3 = 1/9

Thus the probability that the machine fails is 1/9. The probability that the machine works is then the complement of this probability (success = 1-failure), or 1-1/9 = 8/9.

So we pick E.
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Re: A machine is made up of two components, A and B. Each compon [#permalink] New post 10 Aug 2018, 14:42
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No need to encapsulate the answer in the tag [spoiler]

Just leave your reply.

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Re: A machine is made up of two components, A and B. Each compon   [#permalink] 10 Aug 2018, 14:42
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