Loading [MathJax]/extensions/TeX/mathchoice.js

Problem #281

Open Sets

Let n = 192837. For each i from 1 to n, let x_i and y_i be two independently chosen random numbers from (0, 1). Let a_i = \min (x_i, y_i), b_i = \max (x_i, y_i), and S be the intersection of open intervals (a_i, b_i). In other words,

S = \bigcap_{i = 1}^n (a_i, b_i)

It is easy to see that S is itself an open interval. Find the expected length of S.

It can be shown that the answer can be expressed as \frac{p}{q}, where \gcd(p,q) = 1 and q \neq 0 \mod 998244353. Output pq^{-1} \mod 998244353.

Contributed by Yatin Khanna

Solved by 10 users

Log in to submit answers.

Is something wrong?

Maintaining a collection of high quality questions is our top priority. If, however, you do find an error, report the problem and we'll make sure it is reviewed soon.