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 obvious application of probability is to gambling. Not only is this the major historical motivation to study probability, coin flips and rolling dice are still the easiest examples for students to understand while containing very meaty problems (e.g. if a friend flips a coin 20 times and 15 are heads, is the coin biased and how certain can you be? ).