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: 
On a more elementary side, the are these probabilistic paradoxes, such as:
<https://en.wikipedia.org/wiki/Monty_Hall_problem>,
<https://en.wikipedia.org/wiki/Two_envelopes_problem>,
<https://en.wikipedia.org/wiki/Boy_or_Girl_paradox>,
<https://en.wikipedia.org/wiki/Sleeping_Beauty_problem>,
etc.

Also, this one is fun: <https://en.wikipedia.org/wiki/Secretary_problem>
A quincunx (balls dropping through what is typically a triangle of nails, creating a roughly binomial distribution) is fun to watch. Real ones are extremely sensitive to errors in the locations of the nails; there are simulations on the internet, somewhere.