Mathematical Statistics question.

X  1. Suppose we toss a coin 100 times. Let X = the number of heads in the 100 tosses. 

        a. What is the PMF of X? 

         b.   find the probability if X = 50.

          c.  find the probability if X ≤ 50. 

2. A box contains five keys, two of which will open a lock. The keys are randomly selected and tried one at a time until the lock is opened. Keys that do not open the lock are discarded. Let X = the number of the trial on which the lock is opened. Find the expected number of trials until the lock is opened, E[X]. You will need to find the PMF  PMF P(X = x)  in order to do so.