Mathematics
The Binomial Distribution and Its Shape as n Grows
Quick fact
Even for a fair coin (p=0.5), the binomial distribution is perfectly symmetric only when p=0.5, but as n grows, it becomes approximately symmetric regardless of p, thanks to the Central Limit Theorem.
Why this is interesting
Flip a coin 10 times and count the heads—repeat this many times. Why does the shape of your results start to look like a bell curve as you increase the number of flips?