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 1/4, what are the odds of it burning out during the period from 6months to 1 year following its purchase?  Choose the correct choice:
A) 5/27
B) 2/9
C) 1/2
D) 4/9
E) 2/3
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)= 1/4   ---&gt;P( of not burning out in 1st 6 mnth)=1-1/4=3/4   ----&gt;P(of not burning out in a six mnth period)=1/2 *3/4=3/8---&gt;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)   =3/4 * 5/8=1/2   Ans 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 1/4, what are the odds of it burning out during the period from 6months to 1 year following its purchase?