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? Choose the most appropriate option: A) 5/27 B) 2/9 C) 1/3 D) 4/9 E) 2/3
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: 4/9.
<result>D</result>
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?