Odds of bulb burning out

[studentps2011]

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

OA:D
Can anyone explain how this problem can be solved using the theories of probability. Thanks.[spoiler][/spoiler]

[shankar.ashwin]

P(Burning out in 1st 6) = 1/3
P(NOT Burning out in 1st 6) = 2/3

P(NOT Burning out in 2nd 6) = [2/3]/2 = 1/3
P(Burning out in 2nd 6) = 2/3

P(Burning out in 2nd 6) = P(NOT Burning out in 1st 6) * P(Burning out in 2nd 6)

= 2/3 * 2/3 = [spoiler]4/9[/spoiler]

[studentps2011]

Thanks..that's a neat explanation