When to use Binomial versus Beta distribution?

And what is the point of probability distributions anyway?

A footballer is known to score 70% of the penalty kicks he shoots. In the next season we expect him to shoot 10 penalty kicks, how many of them will he score?

He will score 7 out of the 10 penalty kicks, obviously!

Actually, 10 penalty kicks is a very little number to make a definite conclusion from. This obvious 7 could turn up to be 8 or 9 with a bit of luck, or he can miss a couple of unexpected…