True or False? Provide justification if true, or provide a counter example if false:

a)Michael and Kevin are playing a game where Michael scores Xi Geometric(1/m) points and Kevin scores Yi Geometric(1/k) points at round i, independently of other rounds. Then, as the number of rounds goes to infinity, the average total number of points they score per round converges almost surely to m + k.

b) Suppose a random variable X is bounded in [0, 1], and furthermore suppose that E[X] e. Then Pr(X e/2) e/2.