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 6 months to 1 year following its purchase?
A. 5/27
B. 2/9
C. 1/3
D. 4/9
E. 2/3
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Light Bulb Burnout
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Odds of burning out during first 6 months=1/3vodafone 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 6 months to 1 year following its purchase?
A. 5/27
B. 2/9
C. 1/3
D. 4/9
E. 2/3
Odds of not burning out during first 6 months 2/3
Odds of not buring out during second 6 months 1/2 (2/3)=1/3
Odds of burning out during second 6 months 2/3
Choose E.
Thanks, dtweah.
Explanation posted at the Test Preparation Company's website -
If the odds of a light bulb burning out in the first six months are 1/3 , then 2/3 will still be functional after 6 months. Now, if the chance of a light bulb NOT burning out is halved after this first 6-month period, then the odds of it burning out are simultaneously doubled. So the odds that a light bulb which survived the first 6 months will burn out in the period from 6 months to 1 year are no longer 1/3, but 2/3. You now have that 2/3 of the light bulbs survive to the 6-month to 1-year period, and that 2/3 of these will burn out during this time. Multiplying 2/3 by 2/3 you find that the odds of a light bulb burning out during the period from 6 months to 1 year following its purchase are 4/9.
Hence, (D) is correct.
The wordings used in the question tend to lead us to 2/3 as the answer, as posted by dtweah.
Should the answer be 2/3 or 4/9 ?
Or, should the question read as "What are the odds that a lightbulb purchased today will burn out between 6 to 12 months from today? " , if 4/9 is to be the right answer.
Explanation posted at the Test Preparation Company's website -
If the odds of a light bulb burning out in the first six months are 1/3 , then 2/3 will still be functional after 6 months. Now, if the chance of a light bulb NOT burning out is halved after this first 6-month period, then the odds of it burning out are simultaneously doubled. So the odds that a light bulb which survived the first 6 months will burn out in the period from 6 months to 1 year are no longer 1/3, but 2/3. You now have that 2/3 of the light bulbs survive to the 6-month to 1-year period, and that 2/3 of these will burn out during this time. Multiplying 2/3 by 2/3 you find that the odds of a light bulb burning out during the period from 6 months to 1 year following its purchase are 4/9.
Hence, (D) is correct.
The wordings used in the question tend to lead us to 2/3 as the answer, as posted by dtweah.
Should the answer be 2/3 or 4/9 ?
Or, should the question read as "What are the odds that a lightbulb purchased today will burn out between 6 to 12 months from today? " , if 4/9 is to be the right answer.
