Originally Posted by

**shilz222** [snip]

(2) Suppose that the amount of time that a lightbulb works before burning itself out is exponentially distributed with mean ten hours. Suppose that a person enters the room in which the lightbulb is burning. If the person wants to work for $\displaystyle 5 $ hours, what is the probability that he will be able to complete his work without the bulb burning out? What if its not exponential.

Ok so I think $\displaystyle P(\text{remaining lifetime} > 5 ) = e^{-1/2} $ for exponentially distribution. Mr F says: Correct. See also my main reply.

However, now I want to calculate $\displaystyle P(\text{lifetime} > t+5| \text{lifetime} > t) $.

I would think that this would equal $\displaystyle \frac{P(\text{lifetime} > t+5)}{P(\text{lifetime} > t)} $. Mr F says: Correct.