The lifetime of a certain type of batteries follows an exponential distribution with the mean of 12 hours.a) What is the probability that a battery will last more than 14 hours?b) Once a battery is depleted, it is replaced with a new battery of the same type. Assuming independence between lifetimes of batteries, what is the probability that exactly 2 batteries will be depleted within 20 hours?c) What is the probability that it takes less than 30 hours until the forth battery is needed?