## Problem of the Day #145: AlbertAugust 11, 2011

Posted by Sreenath in : potd , trackback

Let S be a sequence of random variables, all 0 or 1, such that the probability of $S_n$ being 0 is $\frac{1}{n^2}$. Let $p$ be the expected value of the probability that the product of the elements of a randomly chosen subsequence of S is nonzero. Find the integer closest to $10000\cdot p$.

You may use any computational aid.