donisback 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 6months to 1 year following its purchase?

A. 5/27

B. 2/9

C. 1/3

D. 4/9

E. 2/3

PLEASE EXPlain.

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

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