I toss $n$ biased coins and I want to count the number of times you get a H followed by a T or a T followed by a H. I call these switches. So for example if I get HHTTHTHHHT then I have $5$ switches in total. If the coin gives H with prob $p$ and $T$ with prob $1-p$ then what is the probability of getting at least $k$ switches?
Update. joriki has given an exact answer. Is there a Chernoff type bound one can get to see if the number of switches is far from the mean? The mean number of switches is $\mu= (n-1)2p(1-p)$, I think.