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Probabilistic methods prove existence results in a nonconstructive fashion, by showing the chance of randomly selecting a solution is greater than zero.

12 votes
12 answers
2k views

What are fun elementary subjects in probability?

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 …
16 votes
1 answer
400 views

Maximal number of subsets in $\{1,\dots,n\}$ such that neither is contained in a union of tw...

What are known estimates for maximal $M$ for which their exists subsets $A_1,\dots,A_M$ in $\{1,\dots,n\}$ such that there do not exist different indexes $i,j,k$ for which $A_i\subset A_j\cup A_k$? I …