OME 1989 Problem 1

An exam at a university consists of one question randomly selected from the $n$ possible questions. A student knows only one question, but he can take the exam $n$ times. Express as a function of $n$ the probability $p_n$ that the student will pass the exam. Does $p_n$ increase or decrease as $n$ increases? Compute $lim_{n\to \infty}p_n$ . What is the largest lower bound of the probabilities $p_n$ ?