You have a flashlight that uses two batteries and you have a package of three new batteries. Suppose that each battery has an independent lifetime (in hours) with exponential(1/50) distribution. Find the distribution of the number of hours T that you can use the flashlight.
Attempt for solution: denote by T the number of hours you can use the flash light let B1, B2 and B3 be the batteries respectively (B1\B2\B3) ~ exp(1/50)
I have the thought that if we use the first two batteries and the first one runs out first, then we have the second and third one once the second one runs out we can't use the flash light so the maximum life of the flashlight would be the amount of time the second battery runs
But i don't exactly know how to put this in terms of probability
I would really appreciate if there is someone out there willing to share ideas