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

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dimri10
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In a panel of 10 light bulbs, the odds of any light bulb to burn out [#permalink] New post   Updated on: 06 Jul 2011, 13:30
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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
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B

Originally posted by dimri10 on 06 Jul 2011, 12:48.
Last edited by dimri10 on 06 Jul 2011, 13:30, edited 1 time in total.
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Re: In a panel of 10 light bulbs, the odds of any light bulb to burn out [#permalink] New post   06 Jul 2011, 12:59
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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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dimri10
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Re: In a panel of 10 light bulbs, the odds of any light bulb to burn out [#permalink] New post   06 Jul 2011, 13:30
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
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Re: In a panel of 10 light bulbs, the odds of any light bulb to burn out [#permalink] New post   08 Aug 2011, 12:52
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).
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Re: In a panel of 10 light bulbs, the odds of any light bulb to burn out [#permalink] New post   03 Oct 2017, 08:56
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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) \(= 1 - (0.94)^{10}\)

Answer (B)
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Re: In a panel of 10 light bulbs, the odds of any light bulb to burn out [#permalink] New post   07 May 2020, 04:31
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Re: In a panel of 10 light bulbs, the odds of any light bulb to burn out [#permalink]
07 May 2020, 04:31
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