A copy machine is used to make n pages of copies per day. The machine has two trays in which paper gets loaded, and each page is taken randomly and independently from one of the other trays. At the beginning of the day, the trays are refilled so that they each have m pages. Using simulations in R, find the smallest value of m for which there is at least a 95% chance that both trays have enough paper on a particular day, for n = 10, n = 100, n = 1000, and n = 10000.