(Solved): Question 9. Suppose that there are 2 batteries, each of which has a lifetime that is independently a ...

Question 9. Suppose that there are 2 batteries, each of which has a lifetime that is independently and exponentially distributed with mean 3 and 5 days respectively. We plug these batteries in a device. It is known that the device stops working if both batteries complete their lifetime. What is the probability that the device will stop working in less than 2 days?