There are two types of batteries in a bin. When in use, type i batteries last (in hours) a...

There are two types of batteries in a bin. When in use, type i batteries last (in hours) an exponentially distributed time with rate λj,i = 1,2. A battery that is randomly chosen from the bin will be a type i battery with probability  If a randomly chosen battery is still operating after t hours of use, what is the probability that it will still be operating after an additional 5 hours?