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: 
I nominate the **Overlapping Words Paradox**. E.g., see pages 42-44 in a [book excerpt](https://stepic.org/media/attachments/lessons/1/excerpt_1st_printing.pdf), a [research paper](http://www.worldscientific.com/doi/abs/10.1142/9789814503655_0006), or an [elementary exposition](http://kvant.mccme.ru/1987/05/luchshee_pari_dlya_prostakov.htm) in Russian Kvant journal.
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.