1. The problem statement, all variables and given/known data We are flipping a coin with probability p of getting heads n times. A "change" occurs when an outcome is different than the one before it. For example, the sequence HTHH has 2 changes. If p=1/2 what is the probability that there are k changes? 2. Relevant equations I've been working with the probability mass function of a binomial random variable: (n C k) pk(1-p)n-k 3. The attempt at a solution For the n flips there are n-1 possible "gaps" between flips when change could occur. I then reasoned that at the end of every flip since you a flipping a fair coin, there is a 1/2 chance of getting a change and a 1/2 chance of not getting a change. My resulting formulation for probability of k changes in n flips was: (n-1 C k)((1/2)k)((1/2)n-k) but I worked out explicitly the probabilities of k changes for n=2, 3, and 4 and this function did not give me at all correct answers. I'm not sure how I should approach it differently.