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

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Intern
Joined: 13 Oct 2009
Posts: 19
Schools: ISB, UCLA,Darden
For each 6-month period during a light bulb's life span, the odds of  [#permalink]

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Updated on: 20 Apr 2015, 07:11
1
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Difficulty:

95% (hard)

Question Stats:

26% (01:38) correct 74% (02:00) wrong based on 137 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

Originally posted by donisback on 17 Dec 2009, 04:42.
Last edited by Bunuel on 20 Apr 2015, 07:11, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Joined: 02 Sep 2009
Posts: 64891
Re: For each 6-month period during a light bulb's life span, the odds of  [#permalink]

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17 Dec 2009, 05:34
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6
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

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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Joined: 09 May 2009
Posts: 139
Re: For each 6-month period during a light bulb's life span, the odds of  [#permalink]

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17 Dec 2009, 06:47
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, 06:58
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

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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Joined: 15 Jan 2017
Posts: 314
Re: For each 6-month period during a light bulb's life span, the odds of  [#permalink]

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13 Dec 2017, 13:15
Lucky2783 wrote:
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

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

Could you explain why 1/2 *2/3 --> where did that derive from?
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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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13 Dec 2017, 13:39
1
Lucky2783 wrote:
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

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

Could you explain why 1/2 *2/3 --> where did that derive from?

The odds of not burning out in the first 6 months are 2/3.

The odds of not burning out over the next 6 month period are half of that. (The problem reads "the odds of it not burning out from over-use are half what they were in the previous 6-month period"). Half of 2/3 is 1/2*2/3 = 1/3.

Likewise, the odds of not burning out over the next 6 month period would be 1/2*1/3 = 1/6, and so on.
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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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15 May 2020, 23:32
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Re: For each 6-month period during a light bulb's life span, the odds of   [#permalink] 15 May 2020, 23:32