If I apply to 10 undergraduate schools what're the odds I get into AT LEAST ONE?

It’s not a lottery. Each college has expectations. You could apply to 40 and win none, if you dont match the basics they need.

Adcoms don’t toss a coin. And OP isn’t speaking of a balanced range of top 100. Rather, among the most competitive. And without the grade or AP consistency and EC patterns, breadth, etc.