The book of Santosh Venkatesh *The Theory of Probability, Explorations and Applications*, Cambridge University Press, 2012  has many   interesting examples that would be accessible to a good high school student.  Let me mention a few to give you a taste.

1. A beautiful probabilistic proof of Cayley's formula on the number of trees.

2. A nice connection between Viete's formula

$$ \frac{\sin x}{x} =\prod_{k=1}^\infty \cos\left(\frac{x}{2^k}\right) $$

and the distribution of digits in the binary expansion of a random number $x\in [0,1]$.

3. Random graphs.

4. Limits on wireless  broadcasting.

The  problems at the end of each chapter  are excellent, of varied degrees of difficulty.