Question: I have to read several lectures on probability or applications of probability for high school students (of high level). There is no necessary part I must lecture, that is, my aim is just advertisement. What are possible subjects? 

There are many nice examples in Alon-Spencer book, with applications to combinatorics and number theory. Is there something in this spirit, but rather on probability itself?

Answer: 
Random walk! That is a fascinating topic which can be treated with combinatorial methods. Associated is the ruin problem. Treat the facts that simple random walk is recurrent in dimension two but not in dimension three.
The Central Limit Theorem and how it even works for something as discrete as counting coin flips.