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

Question

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

Show SpoilerOA

D

PLEASE EXPlain.

A. 5/27
B. 2/9
C. 1/3
D. 4/9
E. 2/3

Bunuel · Accepted Answer

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

Answer: D.

xcusemeplz2009 · Answer

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

Lucky2783 · Answer

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

Madhavi1990 · Answer

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

ccooley · Answer

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.

Kinshook · Answer

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?

Probability of light bulb burning out during the first 6-month period following its purchase = 1/3
Probability of light bulb NOT burning out during the first 6-month period following its purchase = 1-1/3= 2/3

Probability of light bulb NOT burning out during next 6-month period = 1/3
Probability of light bulb burning out during next 6-month period = 1-1/3 = 2/3

Probability of light bulb burning out during the period from 6months to 1 year following its purchase = Probability of light bulb NOT burning out during the first 6-month period following its purchase*Probability of light bulb burning out during next 6-month period = 2/3*2/3 = 4/9

IMO D

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards