Please provide clear explanation and show your steps. Thank you!

1. More Heads than Tails? (9 points) Let X represent the difference between the number of heads and the number of tails obtained when a fair coin is tossed independently 100 times. What are the possible values of X? What is the probability that X = 4? (Note: X = H T, not X = |H T|. That is, if you have more tails than heads, then the difference is negative, not positive.)