You write a software program over and over, and each time there is probability p that it works correctly, independent of previous attempts. Consider the random variable X, number of tries until the program works correctly.

(a) (5 points) Write down the PMF of the random variable X.

(b) (10 points) Show that the it is a valid PMF.

(c) (5 points) Calculate the probability that at least 2 tries needed for the program to work correctly.