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# In a panel of 10 light bulbs, the odds of any light bulb to burn out

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Manager
Joined: 16 May 2011
Posts: 203
Concentration: Finance, Real Estate
GMAT Date: 12-27-2011
WE: Law (Law)
In a panel of 10 light bulbs, the odds of any light bulb to burn out [#permalink]

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06 Jul 2011, 11:48
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Difficulty:

55% (hard)

Question Stats:

57% (00:42) correct 43% (00:53) wrong based on 27 sessions

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In a panel of 10 light bulbs, the odds of any light bulb to burn out are 0.06 at any given 10 minutes. Should a light bulb burn out, the whole panel would instantly turn off. What are the odds that the panel would be turned off within the first 10 minutes after it was switched on?

(A) 1-0.06^10
(B) 1-0.94^10
(C) (1-0.94)^10
(D) 0.06
(E) 1-10*0.06
[Reveal] Spoiler: OA

Last edited by dimri10 on 06 Jul 2011, 12:30, edited 1 time in total.
Manager
Joined: 29 Jun 2011
Posts: 71
Re: In a panel of 10 light bulbs, the odds of any light bulb to burn out [#permalink]

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06 Jul 2011, 11:59
1
KUDOS
IMO B...but is B [1 - (0.94^10)] because thats what I am getting.

solution : consider in 10 minutes space
1 light bulb can go off P = 0.06
so, P that the lightbulb does not go off = 1-0.06 =.94
now we have 10 lightbulbs. Their functioning properly forms a mutually exclusive set of events.
therefore, P that all of them function properly = .94 * .94 (10 times) = .94^10
now, for the whole system to trip even 1 faulty bulb is enough.
therefore, we need P(at least one trips)
which is P(at least one) = 1 - P(none trip) = 1 - P(all function properly) = 1 - 0.94^10
Ans B
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Manager
Joined: 16 May 2011
Posts: 203
Concentration: Finance, Real Estate
GMAT Date: 12-27-2011
WE: Law (Law)
Re: In a panel of 10 light bulbs, the odds of any light bulb to burn out [#permalink]

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06 Jul 2011, 12:30
fivedaysleft wrote:
IMO B...but is B [1 - (0.94^10)] because thats what I am getting.

solution : consider in 10 minutes space
1 light bulb can go off P = 0.06
so, P that the lightbulb does not go off = 1-0.06 =.94
now we have 10 lightbulbs. Their functioning properly forms a mutually exclusive set of events.
therefore, P that all of them function properly = .94 * .94 (10 times) = .94^10
now, for the whole system to trip even 1 faulty bulb is enough.
therefore, we need P(at least one trips)
which is P(at least one) = 1 - P(none trip) = 1 - P(all function properly) = 1 - 0.94^10
Ans B

EDITED. THANK'S FOR NOTICING
Manager
Joined: 14 Feb 2011
Posts: 66
Re: In a panel of 10 light bulbs, the odds of any light bulb to burn out [#permalink]

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08 Aug 2011, 11:52
dimri10 wrote:
In a panel of 10 light bulbs, the odds of any light bulb to burn out are 0.06 at any given 10
minutes. Should a light bulb burn out, the whole panel would instantly turn off. What are
the odds that the panel would be turned off within the first 10 minutes after it was switched
on?
(A) 1-0.06^10
(B) 1-0.94^10
(C) (1-0.94)^10
(D) 0.06
(E) 1-10*0.06

ans B.

Prob that light will not turned off = 0,94^10. Hence prob (turn off) = 1 - prob (not turn off).
Non-Human User
Joined: 09 Sep 2013
Posts: 13832
Re: In a panel of 10 light bulbs, the odds of any light bulb to burn out [#permalink]

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03 Oct 2017, 06:24
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: In a panel of 10 light bulbs, the odds of any light bulb to burn out [#permalink]

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03 Oct 2017, 07:56
dimri10 wrote:
In a panel of 10 light bulbs, the odds of any light bulb to burn out are 0.06 at any given 10 minutes. Should a light bulb burn out, the whole panel would instantly turn off. What are the odds that the panel would be turned off within the first 10 minutes after it was switched on?

(A) 1-0.06^10
(B) 1-0.94^10
(C) (1-0.94)^10
(D) 0.06
(E) 1-10*0.06

P (Panel woud be turned off within first 10 mins) = 1 - P (Panel would not be turned off within first 10 mins)

Only if all 10 light bulbs work will the panel not be turned off within the first 10 mins.
Probability of a light bulb working = 1 - 0.06 = 0.94
Probability of 10 light bulbs working for the first 10 mins $$= (0.94)^{10}$$

P (Panel woud be turned off within first 10 mins) $$= 1 - (0.94)^{10}$$

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Re: In a panel of 10 light bulbs, the odds of any light bulb to burn out   [#permalink] 03 Oct 2017, 07:56
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