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# For each 6-month period during a light bulb's life span, the odds of

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For each 6-month period during a light bulb's life span, the odds of [#permalink]

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17 Dec 2009, 05:42
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Question Stats:

28% (01:01) correct 72% (01:37) wrong based on 135 sessions

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For each 6-month period during a light bulb's life span, the odds of it not burning out from over-use are half what they were in the previous 6-month period. If the odds of a light bulb burning out during the first 6-month period following its purchase are 1/3, what are the odds of it burning out during the period from 6months to 1 year following its purchase?

A. 5/27
B. 2/9
C. 1/3
D. 4/9
E. 2/3
[Reveal] Spoiler: OA

Last edited by Bunuel on 20 Apr 2015, 08:11, edited 1 time in total.
Renamed the topic, edited the question and added the OA.

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Re: For each 6-month period during a light bulb's life span, the odds of [#permalink]

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17 Dec 2009, 06:34
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donisback wrote:
For each 6-month period during a light bulb's life span, the odds of it not burning out from over-use are half what they were in the previous 6-month period. If the odds of a light bulb burning out during the first 6-month period following its purchase are 1/3, what are the odds of it burning out during the period from 6months to 1 year following its purchase?
A. 5/27
B. 2/9
C. 1/3
D. 4/9
E. 2/3

[Reveal] Spoiler: OA
D

I think there should be "probability" instead of "odds" (these two things are not the same and GMAT always asks about probability, not odds).

Probability of not burning out during the first 6 months 1-1/3=2/3
Probability of not burning out during the next 6 months 2/3/2=1/3, hence probability of burning out 1-1/3=2/3.

Probability of burning out during the period from 6 months to 1 year = Probability of not burning out in first 6 months * Probability of burning out in next 6 months = 2/3 * 2/3 =4/9

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Re: For each 6-month period during a light bulb's life span, the odds of [#permalink]

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17 Dec 2009, 07:47
P(of not burning out in a six mnth period)=1/2 of P(of not burning out in prev 6 mnth period)
P(of burning out in 1st 6 mnth)= 1/3
---> P( of not burning out in 1st 6 mnth)=1-1/3=2/3
---->P(of not burning out in a six mnth period)=1/2 *2/3=1/3---> P(of burning out in a six mnth period)=1-1/3=2/3
now
P( of burning out in 2nd six mnth period)=P( of not burning out in 1st six mnth)*P(of burning out in a six mnth)
=2/3 * 2/3=4/9
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Re: For each 6-month period during a light bulb's life span, the odds of [#permalink]

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20 Apr 2015, 07:58
donisback wrote:
For each 6-month period during a light bulb's life span, the odds of it not burning out from over-use are half what they were in the previous 6-month period. If the odds of a light bulb burning out during the first 6-month period following its purchase are 1/3, what are the odds of it burning out during the period from 6months to 1 year following its purchase?
A. 5/27
B. 2/9
C. 1/3
D. 4/9
E. 2/3

[Reveal] Spoiler: OA
D

P(Not Burning out in first 6months) = 2/3
P(Not Burning out in 6months- 12months ) = $$\frac{1}{2} * \frac{2}{3}$$ = $$\frac{1}{3}$$
hence , P(Burning out in 6months- 12months ) = $$\frac{2}{3}$$

P(Not Burning out in first 6months) * P(Burning out in 6months- 12months ) = $$\frac{2}{3}* \frac{2}{3} = \frac{4}{9}$$

Ans: D
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Re: For each 6-month period during a light bulb's life span, the odds of [#permalink]

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28 Oct 2017, 11:31
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Re: For each 6-month period during a light bulb's life span, the odds of   [#permalink] 28 Oct 2017, 11:31
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