Probability of having a good set by choosing independently from Universe

Let $ S$ , $ T$ be two disjoint subsets of a universe $ U$ such that $ |S| = |T| = n$ . Suppose we select a random subset $ R\subseteq U$ by independently sampling each element of $ U$ with probability $ p$ ; that means, for each element $ i$ of $ U$ independently we include $ i$ in $ R$ with probability $ p$ . We say that the random subset $ R$ is good if the following two conditions hold: $ R\cap S = \emptyset$ and $ R\cap T = \emptyset$ . Show that for $ p=1/n$ , the probability that $ R$ is good is larger than some positive constant.