If you guys are struggling with 10 flips, maybe you can reduce it to 2 flips for simplicity. The chance of getting two heads in a row is one in four. Same chance of getting two tails in a row. With three flips, the chance is one in eight, count em. Just add two possibilites to each of the four from the two flip case. Keep adding a flip at a time and youll get to ten. All your fancy z scores dont mean a thing if they give you the wrong answer.
I never would have imagined that I would one day be explaining something to a statistician. Too bad we lost dr. Pepper.