I found this "probability" problem when I read a person's blog.

What's probability that two randomly chosen nature numbers are relatively prime?

It is claimed that there is a very elegant solution for this problem. This problem reminds me another one. Some people asked for an example of a 0-probability …

If we randomly put balls into \(m(\ge1)\) boxes until \(n(\le m)\) of them are occupied, what is the expectation of the number of balls needed?

See my neat solution here.

Suppose there are \(n\) distinct numbers \(x_1,\ldots, x_n\), and \(y_1, \ldots, y_n\) is a random permutations of them. If \(\exists k\) such that \(y_k<y_i, \forall 1\le i<k\), then we say that \(y_k\) is a record (we always count \(y_1\) as a record). What is the expected …

If we randomly put \(n(\ge1)\) balls into \(m(\ge1)\) boxes, what is the expectation of the number of empty boxes?

See my neat answer here.