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

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Bunuel
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A machine is made up of two components, A and B. Each component either [#permalink] New post  14 Aug 2018, 02:32
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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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Re: A machine is made up of two components, A and B. Each component either [#permalink] New post  14 Aug 2018, 04:23
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Bunuel wrote:
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. \(\frac{8}{9}\)


Method 1:

Machine works if atleast one component works i.e. we get the following cases for machine to work

Case 1: First Component works and Second Fails = Probability = (2/3)*(1/3) = 2/9

Case 2: First Component Fails and Second Works = Probability = (1/3)*(2/3) = 2/9

Case 3: First Component works and Second Works = Probability = (2/3)*(2/3) = 4/9

Total Probability = (2/9)+(2/9)+(4/9) = 8/9

Answer: option E

Method 2:

Probability of machine to work = 1 - Probability of machine to fail to wrk

i.e. Probability of machine to work = 1 - Probability of Both components failing = 1- (1/3)*(1/3) = 1- (1/9) = 8/9

Answer: Option E

Hope this helps!!!
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Re: A machine is made up of two components, A and B. Each component either [#permalink] New post  14 Aug 2018, 02:37
Bunuel wrote:
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. \(\frac{8}{9}\)



A works but B doesn't = 2/3*1/3=2/9
B works but A doesn't = 2/9
both A and B work = 2/3*2/3=4/9
p(machine works) = sum of above = 2/9 + 2/9 + 4/9 = 8/9
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Re: A machine is made up of two components, A and B. Each component either [#permalink] New post  14 Aug 2018, 04:37
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The only case in which machine will not work : Both A and B fail

Probability that machine will work = 1 - Probability of both A and B failing

Probability of A failing = 1 - 2/3 = 1/3

Probability of B failing = 1 - 2/3 = 1/3

Probability of both A and B failing = (1/3)*(1/3) = 1/9

Probability that machine will work = 1 - 1/9 = 8/9
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Re: A machine is made up of two components, A and B. Each component either [#permalink] New post  17 May 2023, 19:58
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Re: A machine is made up of two components, A and B. Each component either [#permalink]
17 May 2023, 19:58
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