Suppose you flip a fair coin times. What is the probability distribution for the longest streak of consecutive like outcomes? That is, let
Probability that there exists a streak of consecutive heads or consecutive tails in the sequence of tosses, but no streaks longer than exist.
In case it helps, here is a picture of a coin.
PS – The picture doesn’t help, but Sacagawea was pretty hot for a 15-year old. Also, she apparently had a small, secondary head growing out the back of her neck.