(Solution) - It is known that the lifetime of Save Bucks batteries follows -(2025 Original AI-Free Solution)

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It is known that the lifetime of Save-Bucks batteries follows an Exponential distribution with a mean of 40 hours. The lifetime of LittleMoola batteries follows an Exponential distribution with a mean of 30 hours.
a. What is the probability a SaveBucks battery will last more than 48 hours?
b. What is the probability a LittleMoola battery will last more than 48 hours?
c. Given that a SaveBucks battery has lasted more than 48 hours, what is the probability it will last more than 96 hours? What property applies to this sit nation?
d. The batteries look identical, so if you have a battery you selected at random which has lasted more than 48 hours, what is the probability it is s SaveBucks battery? Which rule do you use to answer this question?