Problem Solving

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?

5/27
2/9
1/3
4/9
2/3

Is it C?

rishianand7 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?

5/27
2/9
1/3
4/9
2/3

p(no burn now) = 1/2 * p(no burn in the previous 6-month period)
1-p(burning out now) = 1/2 * (1 - p(burning out in the first six months))
1 - P = 1/2 * (1 - 1/3)
1 - P = 1/2 * 2/3
1 - P = 1/3
P = 2/3

Choose E

Cheers

Brent@GMATPrepNow wrote:

rishianand7 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?

5/27
2/9
1/3
4/9
2/3

I'm not too crazy about the wording of this question, since there's a big difference between ODDS and PROBABILITY

Probability = (favorable outcomes)/ (total outcomes)
Odds = the ratio of favorable outcomes to unfavorable outcomes

So, for example, if we randomly select a number from {3, 5, 7, 9, 11}, then . . .
- The PROBABILITY of selecting a prime number = 4/5
- The ODDS in favor of selecting a prime number = 4:1

I don't think I've ever seen the GMAT use the term "odds" (other than in the context of even and odd integers).

Having said all of that, if we take the question and replace "odds" with "probability" then ganeshrkamath's solution is perfect (as always )

Cheers,
Brent

Thanks Brent.

Taking your definition of odds,
Odds of a light bulb burning out during the first 6 month period = 1/3
Odds of a light bulb NOT burning out during the first 6 month period = 3/1

Odds of a light bulb NOT burning out during the next 6 month period = 3/2
Odds of a light bulb burning out during the next 6 month period = 2/3

The answer is still the same: E

Cheers

Here's the explanation from Kaplan.

"If the odds of a light bulb burning out in the first six months are , then 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 , but . You now have that of the light bulbs survive to the 6-month to 1-year period, and that of these will burn out during this time. Multiplying by , you find that the odds of a light bulb burning out during the period from 6 months to 1 year following its purchase are . (D) is correct."

Safe to say this won't be on the GMAT?